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UNIVERSITY OF TRENTO

SCHOOL OF SOCIAL SCIENCES

DOCTORAL SCHOOL IN ECONOMICS AND MANAGEMENT

EMPIRICAL ESSAYS ON THE

ECONOMICS OF FOOD PRICE SHOCKS:

MICRO-ECONOMETRIC EVIDENCE FROM UGANDA

A DISSERTATION

SUBMITTED TO THE DOCTORAL SCHOOL OF ECONOMICS AND MANAGEMENT

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DOCTORAL DEGREE

(PH.D)

IN ECONOMICS AND MANAGEMENT

Adamon Ndungu Mukasa

April 2015

2

THESIS SUPERVISOR

Professor Gabriella Berloffa

University of Trento, Italy

EXTERNAL COMMITTEE

Professor Stephan Klasen

University of Göttinger, Germany

Professor Carlo Federico Perali

University of Verona, Italy

FINAL COMMITTEE

Professor Carlo Federico Perali

University of Verona, Italy

Professor Luciano Fratocchi

University of L’Aquila, Italy

Doctor Matteo Ploner

University of Trento, Italy

iv

Contents List of Tables, Figures, and Appendices ................................................................................................ vii

Acknowledgements .................................................................................................................................. xi

Summary and Overview.......................................................................................................................... xii

ESSAY I FOOD PRICE VOLATILITY IN UGANDA: TRENDS, DRIVERS, AND SPILLOVER

EFFECTS ................................................................................................................................................ 1

1.1 Introduction ................................................................................................................................... 2

1.2 Patterns of food price indices in Uganda ....................................................................................... 6

1.2 Econometric models of conditional volatility, asymmetric and spillover effects, and drivers of

price volatility ................................................................................................................................... 12

1.2.1 Conditional volatility model ................................................................................................. 13

1.2.2 Asymmetric and leverage effects ......................................................................................... 15

1.2.3 Volatility spillover model ..................................................................................................... 16

1.2.4 Model of drivers of food price volatility .............................................................................. 16

1.3 Data ............................................................................................................................................. 19

1.4 Empirical results .......................................................................................................................... 21

1.4.1 Conditional price volatility ................................................................................................... 21

1.4.2 Asymmetric and leverage effects in food price volatility ..................................................... 28

1.4.3 Volatility spillover effects .................................................................................................... 29

1.4.4 Effects of macroeconomic factors on changes in food price volatility ................................ 31

1.5 Conclusions ................................................................................................................................. 35

ESSAY II WELFARE EFFECTS OF FOOD PRICE CHANGES IN UGANDA UNDER NON-

SEPARABILITY: HOW RELEVANT IS THE NET MARKET POSITION? ................................... 37

2.1 Introduction ................................................................................................................................. 37

2.2 Theoretical model ........................................................................................................................ 39

2.3 Estimation strategy ...................................................................................................................... 46

2.3.1 Estimation of the shadow wage and test of the recursivity hypothesis ................................ 46

2.3.2 Food demand system ............................................................................................................ 48

2.4 Data and descriptive statistics ..................................................................................................... 50

2.4.1 Samples ................................................................................................................................ 50

2.4.2 Consumer prices, commodity grouping, and consumption shares ....................................... 51

2.4.3 Identification of the household’s food market position ........................................................ 55

2.5 Results and discussion ................................................................................................................. 61

2.5.1 Estimation of shadow wages and separability test ............................................................... 61

2.5.2 Demand elasticities ............................................................................................................... 65

2.5.3 Welfare effects of price changes .......................................................................................... 71

2.6 Conclusions ................................................................................................................................. 79

Empirical Essays on the Economics of Food Price Shocks

v

ESSAY III HOW STRONGLY DO AGRICULTURAL RISKS AND FARMERS’

EXPECTATIONS INFLUENCE ACREAGE DECISIONS? DYNAMIC MODELS OF LAND USE

IN UGANDA ........................................................................................................................................ 82

3.1 Introduction ................................................................................................................................. 82

3.2 Theoretical model ........................................................................................................................ 85

3.3 Empirical specification ................................................................................................................ 89

3.3.1 Dynamic multivariate selection model ................................................................................. 91

3.3.2 Dynamic acreage share model .............................................................................................. 92

3.4 Data and construction of variables .............................................................................................. 96

3.4.1 Plot size ................................................................................................................................ 96

3.4.2 Representation of price expectations and risks..................................................................... 98

3.4.3 Expected yields and yield risks .......................................................................................... 100

3.5 Empirical results ........................................................................................................................ 101

3.5.1 Dynamic multivariate crop selection model ....................................................................... 101

3.5.2 Dynamic acreage share model ............................................................................................ 105

3.6 Predictability performance ........................................................................................................ 111

3.7 Conclusions ............................................................................................................................... 114

ESSAY IV WELFARE GROWTH, POVERTY TRAPS, AND DIFFERENTIAL EXPOSURE TO

FOOD PRICE SHOCKS: EVIDENCE FROM UGANDA ................................................................ 115

4.1 Introduction ............................................................................................................................... 115

4.2 Literature review: shocks, welfare dynamics, and poverty traps .............................................. 117

4.3 Empirical evidence on poverty traps ......................................................................................... 120

4.4 Conceptual model ...................................................................................................................... 121

4.5 Data ........................................................................................................................................... 125

4.5.1 Construction of a food price shock variable ....................................................................... 126

4.5.2 Asset index ......................................................................................................................... 130

4.5.3 Descriptive statistics ........................................................................................................... 132

4.5.4 Poverty dynamics, stochastic, and structural poverty......................................................... 134

4.6 Estimation methods and results ................................................................................................. 136

4.6.1 Propositions ........................................................................................................................ 136

4.6.2 Parametric models of consumption and asset dynamics .................................................... 139

4.6.3 Non-parametric models of consumption and asset dynamics............................................. 150

4.6.4 Semi-parametric methods ................................................................................................... 152

4.6.5 Shifts in welfare equilibria, exposure to food price shocks, and regional heterogeneity ... 154

4.6.6 Sensitivity of estimation results to the definition of shock variable ................................... 158

4.7 Conclusions ............................................................................................................................... 159

References ........................................................................................................................................... 163

Appendices .......................................................................................................................................... 185

Contents

vi

Appendix A Additional data and estimation results for Essay I ........................................................ 186

Appendix B Additional data and estimation results for Essay II ...................................................... 191

Appendix C Additional data and estimation results for Essay III ..................................................... 198

Appendix D Additional data and estimation results for Essay IV ..................................................... 210

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List of Tables, Figures, and Appendices

Tables 1.1 Caloric intakes and consumption of main staple foods (2000 – 2011) ............................................. 3

1.2 Unconditional price volatility of key food commodities in Uganda (2000m1 –2012m12) ............ 21

1.3 Optimal endogenous break dates of food price series in Uganda .................................................... 24

1.4 Bai-Perron’s unit root tests in the presence of structural breaks in food prices .............................. 26

1.5 Results of the GARCH (1, 1) model estimation .............................................................................. 27

1.6 EGARCH (1, 1) estimation results, Monthly data, 2000 – 2012 ..................................................... 28

1.7 Responses after one month of price volatility to Cholesky one SD shocks .................................... 30

1.8 Determinants of changes in food price volatility in Uganda – SUR model .................................... 33

1.9 F – tests on restrictions across food commodities ........................................................................... 35

2.1 Theoretical effects of an increase in food prices on food consumption, by net positions in food and

labor markets ......................................................................................................................................... 43

2.2 Changes in real consumer prices of commodity groups between 2005/6 and 2010/11 ................... 53

2.3 Food consumption shares and proportion of zero consumption by commodity groups .................. 54

2.4 Household characteristics by year and net market position ............................................................ 58

2.5 Decomposition of Ugandan households by their net position in the food and labor markets ......... 61

2.6 Stochastic production frontier estimates ......................................................................................... 62

2.7 Technical inefficiency estimation results ........................................................................................ 63

2.8 Summary statistics for w , LPRM ˆ , IA ˆ , and *w ............................................................................. 64

2.9 Expenditure elasticities by survey round, net market position, and (non-) separability .................. 67

2.10 Own-price Hicksian elasticities by net market position ................................................................ 70

2.11 Direct welfare effects of price changes between 2005/6 and 2010/11 under separability (SM) and

non-separability (NSM) (CV as a % of initial household expenditures) ............................................... 72

2.12 Total welfare effects of price changes between 2005/6 and 2010/11 under separability (SM) and

non-separability (NSM) (CV as a % of initial household expenditures) ............................................... 74

2.13 Dynamics of food net market position between 2005/6 and 2010/11 ........................................... 78

2.14 Net market position switching movements and welfare effects of price changes ......................... 79

3.1 Bivariate transition matrices of changes in the distribution of total land holdings ......................... 97

3.2 Coefficient estimates-Dynamic Multivariate Probit model ........................................................... 103

3.3 Acreage elasticities of expected prices and yields and their related risks- Static vs Dynamic models

............................................................................................................................................................. 107

3.4 Equiproportional elasticities - Static vs Dynamic models ............................................................. 109

3.5 Effects of agro-climatic variables and farmer’s characteristics ..................................................... 110

3.6 Observed versus predicted acreage shares .................................................................................... 111

3.7 Comparison between predicted and observed optimal crop choice .............................................. 113


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4.1 Household characteristics by exposure to food price shocks ........................................................ 129

4.2 Summary statistics by survey rounds ............................................................................................ 133

4.3 Percentage of households by poverty dynamics by region: Spells approach ................................ 134

4.4 Poverty transition matrices ............................................................................................................ 136

4.5 Two-step system GMM estimation of consumption growth model .............................................. 143

4.6 Two-step system GMM estimation of asset index growth model ................................................. 147

4.7 Conditional convergence tests of welfare dynamics: Two-step GMM estimations ...................... 150

4.8 Approximate locations of real consumption equilibria by estimation methods ............................ 155

4.9 Approximate locations of asset index (in PLUs) equilibria by estimation methods ..................... 158

4.10 Sensitivity of welfare equilibria to the definition of the price shock variable ............................. 159

List of Tables, Figures, and Appendices

ix

Figures

1.1 Monthly real food price volatility, January 2000 – December 2012 ................................................. 4

1.2 Monthly consumer price indices, July 1997 – December 2012 (Base: 2005/06=100) ...................... 7

1.3 Growth rates of monthly consumer food price indices (July 1997 – September 2007) .................... 8

1.4 Average rainfall levels (in mm) in Uganda (2007 – 2010).............................................................. 10

1.5 Evolution of quarterly fuel pump inflation in Uganda, September 2007 – September 2010 .......... 11

1.6 Evolution of nominal and real effective exchange rates UShs/$US (July 1997- March 2013) ....... 12

2.1 Non-parametric estimates of the relationship between compensating variations and household

expenditures (2005/6-2009/10) – Separable models ............................................................................ 76

4.1 Scatterplot of asset index ............................................................................................................... 132

4.2 Hypothetic relationships between welfare dynamics and exposure to food price shocks ............. 138

4.3 Consumption and asset dynamics: Predicted values using parametric methods ........................... 149

4.4 Consumption dynamics: LOWESS estimates and Kernel-weighted local polynomial smooth .... 152

4.5 Asset dynamics: LOWESS estimates and Kernel-weighted local polynomial smooth ................. 152

4.6 Semi-parametric penalized spline regression estimation: Consumption and asset dynamics ....... 154


x

Appendices

A.1 Monthly price volatility plots (January 2000 – December 2012) ................................................. 187

A.2 Monthly price volatility by main agricultural seasons, 2000m1 – 2012m12 ............................... 188

A.3 Estimated results of Multivariate VARs ....................................................................................... 189

A.4 Matrix of pairwise correlations of food price volatilities ............................................................. 190

B.1 Testing and correcting for attrition in the Uganda National Panel Surveys ................................. 192

B.2 Demand elasticities under separability ......................................................................................... 196

B.3 Estimated average shadow elasticities by food net market position ............................................. 197

C.1 Patterns of crop choice combinations, 2005 – 2012 ..................................................................... 199

C.2 Farmer’s characteristics by GPS measurement status (2005/6 and 2009/10) ............................... 200

C.3 Farmer’s characteristics by GPS measurement status (2010/11 and 2011/12) ............................. 201

C.4 OLS estimation results of observed GPS-based plot area measures (in acres) ............................. 202

C.5 Estimated ARIMA models for monthly real price series 1999 (9) – 2012 (12) ........................... 203

C.6 Unbiasedness tests of expected-price formation hypotheses (OLS estimation) ........................... 204

C.7 Definition and descriptive statistics of relevant variables ............................................................ 205

C.8 Dynamic Multivariate fractional logit estimation results – Models with (I) and without (II)

unobserved heterogeneity .................................................................................................................... 206

C.9 Static Multivariate fractional logit estimation results – Models with (I) and without (II)

unobserved heterogeneity .................................................................................................................... 208

D.1 Cumulative distributions and growth rates of households’ welfare ............................................. 211

D.2 Test of equality between households above and below the vulnerability index hvul .............. 212

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Acknowledgements

From the conception to the finalization and the choice of appropriate methodological

approaches, the validation of the theoretical framework and models to be estimated, the access

to relevant scientific articles, the permanent challenges and recurrent problems that sometimes

lead to discouragement, this thesis has been an exercise both perilous and exciting. It crowns

more than three years of efforts, abnegation, and major challenges both intellectually and

scientifically that introduced me to rigorous scientific research.

Though individually presented, this thesis would have been impossible without the precious

contributions of multitude of people who have somehow participated to its elaboration

through their advice and helpful support. I would like to start by expressing my deepest and

heartfelt gratitude to my supervisor, Professor Gabriella Berloffa, for her rigorous guidance

and encouragement since our first meeting. Your advice and open and constructive criticism

during our countless meetings and discussions have been invaluable in shaping this

dissertation and strengthening my analytical tools. You did not manage your efforts to read

for the umpteenth time all my drafts. Thank you for co-authoring the second paper of this

thesis and for your firm supervision yet in a kind and relaxed spirit.

I am also thankful to Professor Christopher Barrett for this mentoring during my 6-month stay

at the Charles H. Dyson School of Applied Economics and Management of Cornell

University. Thank you for your comments on the earlier versions of my work and for your

advice about the post-doctoral life. I also owe my gratitude to all participants of the weekly

Development Microeconomics’ Seminars at Cornell University for their helpful comments,

especially Megan Sheahan, Linden McBride, Jess Cisse, Kibrom Hirfrfot, Joanna Upton, and

Paul Christian.

An earlier version of essay II was presented at the “Graduate School Association Summer

Conference” of the Dyson School of Cornell University July 17, 2014 and at the “First

SITES-IDEAS Conference” held at the University of Florence September 12, 2014. Essay III

was presented at the “2nd

Bordeaux Workshop in International Economics and Finance-Price

risk management of agricultural commodities in developing countries” held at the Université

de Bordeaux December 5, 2014. I am grateful to the participants of these three conferences

for their instructive comments and suggestions that undoubtedly improved this thesis.

This Ph.D project would not have been possible without the generous grant from the

University of Trento which I duly acknowledge and the support from administrative staff of

Acknowledgements

xii

the School of Social Sciences, in particular Davide Santuari and Nicole Bertotti who were

always prompt to help. I benefited a lot from all the courses I took and seminars I attended

during my stay at the University of Trento. I therefore wish to thank all my teachers:

Christopher Gilbert, Luigi Mittone, Kumaraswamy (Vela) Velupillai, Stefano Zambelli,

Maria-Luigia Segnana, Ugo Trivallato, Luigi Bonatti, Andrea Fracasso, Luciano Andreozzi,

and Emanuele Taufer. I also acknowledge the special moments that I shared with my fellow

students at Trento. To my colleagues in both the Economics and Management (Teddy, Maria,

Marianna, Vahid, and Svetlana) and Development Economics and Local Systems programs

(Zerihun, Muluken, Getahun, and Zubair), thanks for your friendship and for creating a

collegial atmosphere.

My sincere gratitude also goes to my alma mater, the Université Catholique de Bakavu, and

all the members of the department of economics and management, in particular Professors

Jean-Baptiste Ntagoma and Albert Lukuitshi Malaika, for their support and precious advice.

Jean-Baptiste, I still remember the autograph you wrote when you handed me a copy of your

own thesis. Now, I can proudly ensure you that your wish has come true. My special thanks to

Janvier Kilosho with whom I started my university studies and who has become more than a

friend. Please find in this dissertation an inspiration to complete your own Ph.D.

Outside the academic corridors, I received immeasurable love, prayers and support from

family and friends. My special thanks, however, go to my family for their unconditional

moral support and endless love since I embarked in this “lonely project”. I say thank you to

my parents Ndungu Mukasa and Nankafu Muderhwa for being always present throughout my

life, for the support, sacrifice, and advice. To my brothers, Jackson and Christian, and my

sisters, Aline, Yzabel, Rachel, and Naomi, thank you for understanding and respecting my

aspirations. I will never forget your prayers and support even though we have been far apart

since 2010. To the extended Mukasa, Muderhwa, Shamavu, and Bavurhe families all over the

world, I am overwhelmed by your encouragement, self-less hospitality, and unconditional

love every time I needed them.

Adamon N. Mukasa,

April 2015

xiii

Summary and Overview

The vast majority of households in developing countries are located in rural areas and still

depend on agriculture as their main income generating activity. Despite economic progress

was recently achieved by many of these countries at the macroeconomic level, welfare

indicators remain at critical levels for a large proportion of their populations. The absence of

well-functioning insurance and credit markets coupled with the prominence of different

covariate and idiosyncratic shocks (droughts, floods, inflation, conflicts, and health-related

shocks) exacerbate the vulnerability of the poorest among these households. Under such

circumstances, a general consensus among development practitioners has been that policy

interventions will only be effective if they help households prepare for and protect themselves

against stressors and shocks, mitigate ex post their potential losses, and reinforce their

abilities to respond adequately to future threats to their well-being. This goal can only be

achieved if we understand the deep causes that trigger those shocks and the ways in which

they affect households with different initial conditions and characteristics, in particular the

processes through which they prevent some households from moving out of poverty or thrust

some others into spirals of destitution and poverty.

This thesis explores several issues related to our understanding of the causes, consequences,

and households’ responses to different shocks and stressors. One particular type of shocks is

at the core of this dissertation, namely food price shocks. Indeed, the recent sharp increases in

food and other commodity prices between 2006 and 2008 and again in 2011 have generated

passionate debates about their potential drivers and consequences on households, especially in

developing countries. Some of these countries reported social tensions and turmoil, food riots

or social unrest as a direct result of rising food prices while simulations across different

countries have revealed that many vulnerable households even reduced their calorie intakes

(Bellemare, 2015). The four closely related studies of this thesis address respectively the

following research questions:

1. What macroeconomic and environmental drivers explain changes in food price

volatility observed in Uganda between 2000 and 2012? Subsequently, how strong is the

evidence of spillover, asymmetry, and seasonality effects in these volatilities?

2. To what extent are the econometric estimates of welfare effects of food price shocks

sensitive to models’ assumptions, in particular to the incorporation of both labor market

frictions and households’ net positions in food and labor markets?


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3. How do agricultural and market-related risks as well as farmers’ expectations about

future output prices and yield levels shape their crop choice and acreage allocation decisions?

4. How strong is the link between poverty traps and differential exposure and

vulnerability to food price shocks?

This dissertation is motivated by the following gaps in both the theoretical and empirical

literature on food price shocks that are epitomized in the above questionings. First, studies on

food price volatility in developing countries in general, and in Sub-Saharan Africa (SSA) in

particular, have mainly focused on the extent of price transmission between international and

domestic markets and have applied simulation models to identify the poverty impacts of such

price transmission. In regards to the drivers of the observed price volatilities, most empirical

studies typically enumerate a list of potential candidates without quantifying the differential

contribution of each of them. Accordingly, the main purpose of essay I, titled Food price

volatility in Uganda: Trends, Drivers, and Spillover effects, is to fill this empirical gap by

modeling changes over time of food price volatilities and identifying its potential drivers by

means of time-series econometrics. The motivation that propelled this study in Uganda was

guided by the observed increases in consumer food price indices since 2008 despite the

landlocked position of the country and the relatively small price transmission from

international to its domestic food markets, which is an indication that internal or regional

rather than international factors might have been at work. Furthermore, Uganda is among the

rare countries in SSA to have a rich history in gathering household and food price data.

This first essay has a fourfold objective. The first objective checks the claim that increases in

food price levels since 2006 were also accompanied with rises in price volatilities. The second

objective is to analyze the patterns of conditional food price volatilities between 2000 and

2012; the third is to model and test for the presence of spillover and leverage effects in food

price volatilities and the fourth is to model the potential macroeconomic and environmental

drivers of observed food price volatilities and uncover their differential effects.

The analysis is applied to six of the main staple foods produced and consumed in Uganda:

matooke, cassava, maize, potatoes, beans, and millet flour. The graphical representation of

consumer food price indices shows that food prices were astonishingly stable between 2000

and 2007 before starting a rapid upward trend thereafter. Results from variance equality tests

further reveal that for the majority of commodities under investigation (5 out of 6), the

unconditional price volatility (measured by the standard deviation of the price returns) did

effectively increase since January 2008. This implies that from that period onwards, Ugandan


xv

households have entered phases of higher uncertainties and instabilities regarding food prices.

And since high volatility generally implies large and/or rapid changes in food prices, it

became more challenging for producers to make optimal decisions concerning input and land

allocations, while consumers (most of them also producers) may have increased difficulties in

planning their future consumption decisions. The empirical findings also indicate limited

evidence in favor of asymmetric and leverage effects in food price volatilities for about half of

the staples. In addition, no clear picture is portrayed in regards to the nature and extent of

volatility spillover effects across food markets in Uganda, with most of them being only

unidirectional. Finally, this first essay reveals that changes in consumer price indices, rainfall

and fuel volatilities were the main drivers of observed changes in historical food price

volatilities and their impacts were particularly important during periods of high price

instabilities. Gven these findings, the essay highlights the importance of mixing actions that

target primarily the agricultural sector with more global interventions likely to ensure price

stabilization or, at least, reduce price volatility.

The second main research question is tackled in essay II (co-authored with Gabriella

Berloffa) titled Welfare effects of food price changes in Uganda under non-separability: How

relevant is the net market position? This study incorporates the insights from the agricultural

households’ literature (Singh et al., 1986; Strauss, 1986; de Janvry et al., 1991; Taylor and

Alderman, 2002) to identify welfare effects of food price changes in Uganda. The study is

motivated by the lack of both theoretical and empirical work that explicitly takes account of

market failures when analyzing those effects. The study shows that although there exists an

abundant empirical literature on welfare impacts of food price shocks (and especially since

the global food price crisis of 2007/8), these studies generally fall short of recognizing a

crucial feature of markets in developing countries, namely the presence of important market

frictions and failures (Barrett and Carter, 2013) that may lead to deviations from the standard

neoclassical model of rational consumers. The essay demonstrates theoretically that the

effects of food price changes on consumption levels are not straightforward when we allow

for the possibility of labor market imperfections and disaggregate households by their net

positions in the food and labor markets. As a consequence, it becomes a priori impossible to

identify the welfare effects of price changes which may be over- or under-estimated when we

assume perfect functioning food and labor markets.

Methodologically, this second study uses household panel dataset collected in three waves

(2005/6, 2009/10, and 2010/11) to investigate the impacts of allowing for labor market


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frictions and to identify groups of households that lost or gained from food price shocks. To

that end, the essay estimates a panel stochastic production frontier function using the Battese

and Coelli’s (1995) Maximum likelihood estimator and applies the Sherlund et al.’s (2002)

and Barrett et al.’s (2008) approaches to compute shadow wages for non-labor market

participants. It tests for the separability hypothesis using the Kolmogorov-Smirnov and the

Epps-Singleton tests of distributions’ equality between market wages of off-farm workers and

shadow wages of self-employed agricultural households.

In order to estimate the welfare effects of food price changes, the study relies on the

econometrics of demand systems’ estimation using the Quadratic almost ideal demand system

(QUAIDS) of Banks et al. (1997). It is a flexible functional form that incorporates nonlinear

effects and interactions of price and expenditures in the demand relationships. Furthermore, it

is a hybrid model where some goods face a nonlinear expenditure specification (QUAIDS)

while other goods face a linear specification (AIDS). I estimate expenditure and price demand

elasticities for 10 key commodities and commodity groups plus leisure time using the

QUAIDS model. The demand systems are estimated using a Non-linear Seemingly Unrelated

Regression (NSUR) model taking account of censoring in food consumption and the

endogeneity of both households’ expenditures and shadow wage. The QUAIDS is estimated

for each panel wave to check whether households reacted differently to food price changes in

periods of low and high price volatility as outlined in the first essay.

Demand estimates are provided for each sub-group of households to take into consideration

their potential heterogeneous behavior regarding price changes. Accordingly, households are

categorized into 5 groups: non-agricultural households, significant net seller, significant net

buyers, insignificant net sellers, and insignificant net buyers. These last 4 sub-groups are

defined using a 50%-threshold rule: for instance, an agricultural household is a significant net

seller (net buyer) if the total values of its crop sales (of matooke, maize, potatoes, cassava,

beans, rice, millet, sorghum, fruits and vegetables) is at least 1.5 times larger (lower) than

their total market purchases of the same crops.

Estimates of compensating variations using estimated price elasticities computed under

perfect and imperfect labor markets reveal that the welfare effects of food price changes are

globally lower in the non-separable model and different in signs and magnitudes for the sub-

groups of households. In particular, the results show that the welfare effects even present

opposite signs in the sub-period 2005/6-2009/10. Indeed, while Ugandan households as a

whole have benefited from high food price increases between 2005/6 and 2009/10 by 15.4%


xvii

(meaning that they have to decrease their total expenditures of 2009/10 by 15.4% to reach the

utility level achieved in 2005/6), they lost from these price increases by 9.7% if we

incorporate virtual or shadow effects due to labor market frictions. By and large, the findings

from this second essay indicate that non-agricultural, poor, and urban households have

suffered from price increases while among agricultural households, only significant net sellers

and, to a small extent, marginal net sellers have benefited from the price upsurges. However,

the magnitudes of these welfare effects are found to be slightly less important than those

obtained previously through price simulations.

In settings characterized by the prominence of shocks, the uncertainty about the future, and

the quasi-absence of formal insurance and credit markets, agricultural households in most

developing countries can only rely on informal mechanisms or crop diversification strategies

to protect themselves against high variances in food prices (Fafchamps, 1992). Essay III,

titled How strongly do agricultural risks and farmers’ expectations influence acreage

decisions? Dynamic models of land use in Uganda, explores the question of crop choices and

land allocations in environments where farmers face uncertainties about end-of-season output

prices and yield levels, weather variability, and formulate expectations about their future

levels. In particular, this essay answers the following empirical questions: Are Ugandan

farmers more sensitive to changes in expected prices or expected yields? Or is it the volatility

of prices and yields that finally matters? Do farmers keep growing the same crop once it has

been selected previously or do they instead take advantage of crop rotational effects? Which

factors—household characteristics (such as education, sex, or household size), environmental

factors (such as land quality, typology of soil, or irrigation practices), or agricultural and

market-related risks—are most important when it comes to selecting and allocating land to

particular crops?

To that end, I estimate two econometric models: a multivariate crop selection model that

analyses the factors affecting the probability of selecting and growing different crops under

market uncertainties and a conditional acreage share model that investigates how farmers

allocate their agricultural land to different crops so that to maximize the expected utility of

their profit. In these models, the choices that the farmers made in the past regarding the crops

they grew and how much land they allocated to different crops are assumed to influence

current farmers’ choices, leading to dynamic crop choice and land allocation problems.

Moreover, farmers’ behavior is modeled as a generalized two-step Heckman-type approach

consisting in a sequential decision: first they select the crop (s) to grow and second, they


xviii

determine the proportion of land to share out among the selected crops. The model

specifications allow to distinguish true state dependence in crop choice and land allocation

from spurious state dependence (due to unobserved heterogeneity) and to check for the

presence of inertia effects (if farmers do not change their previous crop choice patterns) or

spillover/rotational effects (if choices made in the past by a farmer regarding one crop affect

current decisions about competing crops). Both the selection and land share models are

estimated for 6 crops or crop groups, matooke, cassava, maize, potatoes (both Irish and sweet

potatoes), beans, and other cereals (rice, millet, and sorghum), as well as a residual category

for all other crops not selected in the present analysis using panel dataset of 1,598 agricultural

households over 4 periods.

To take account of initial observations problem posed by the dynamic nature of the farmers’

decisions, I apply in both crop choice and acreage allocation models the Wooldridge’s (2002)

recommendation by including as an additional covariate the first observations of each

dependent variable. Furthermore, to deal with farm and crop unobserved heterogeneity, I

apply the Mundlak-Chamberlain approach by assuming that unobserved heterogeneity can be

specified as a linear function of the average values of all time-varying independent variables.

The crop selection problem is then modeled as a dynamic multivariate probit regression and

estimated through Simulated Maximum Likelihood and the G (Geweke) H (Hajivassiliou) K

(Keane) simulator; whereas the conditional acreage share model is estimated using a dynamic

multivariate fractional logit model (Mullahy, 2011).

The empirical findings suggest that price, yield, and weather risks are more important than

their expected values in both crop choice and acreage share models. Farmers are found more

sensitive to changes in expected yields and yield volatility than in expected prices or price

volatility. Moreover, most conditional expected acreage share elasticities in the static models

are overestimated compared to the dynamic models and finally, I find evidence of strong state

dependence in farmers’ crop choices and acreage allocations while the presence of rotational

effects is relatively limited compared to inertia effects.

The final essay, titled Welfare growth, poverty traps, and differential exposure to food price

shocks: Evidence from Uganda, explores the last main research question of this dissertation

by investigating the link between poverty traps, poverty persistence, and differential exposure

and vulnerability to food price shocks using four waves of Uganda National Panel Surveys

(UNPS) spanning over the years 2005-2012. The motivation behind this last essay is the

unproved claim that food price shocks, especially since the recent global food price crisis,


xix

might have thrust thousands, or even millions, of households in most developing countries

into chronic poverty and have even exacerbated the risk of being trapped into poverty (Martin

and Ivanic, 2008). The essay develops a modified Ramsey consumption growth model

allowing for reference-dependent preferences and both food price and asset shocks to model

theoretically the impact of shocks on welfare growth. To uncover the link between exposure

to food price shocks and the patterns of welfare growth dynamics, the study first constructs

both household-specific food price shocks’ variable and asset index (using a livelihood-based

regression model). Three types of econometric methods (parametric, non-, and semi-

parametric) are then applied to check for the hypothesis of food-price-shocks-induced poverty

traps.

Under parametric methods, consumption and asset dynamics are modeled as cubic polynomial

regressions of lagged consumption levels and asset indices, respectively, and estimated by the

two-step system Generalized Methods of Moments (S-GMM). During these estimations, I test

for the existence of serial correlations of error terms using the Arellano-Bond first order AR

(1) and second order AR (2) tests, and check for over-identification of the instruments

through the Hansen J test. To allow for nonlinearities in the effects of food price shocks, I

enter the price shocks’ variable both linearly and interacted with the degree of the household’s

vulnerability to food price shocks. This latter is computed using the principal components

analysis by incorporating three factors likely to determine the extent of this vulnerability,

namely the food dependency ratio, the degree of market participation, and the level of

household’s income.

The results suggest the presence of nonlinearities in both consumption and asset dynamics.

Furthermore, I find that changes in the degree of exposure to food price shocks tend to

decrease the rates of both consumption and asset growth during the sample period, with the

effects being more important in the consumption growth model. Concretely, the parametric

results show that the consumption growth rate is on average marginally decreasing with the

degree of exposure to food price shocks, and this effect is increasing with the extent of

household’s vulnerability. The vulnerability threshold to food price shocks is found to be

1.364, meaning that on average the effect of food price shocks starts inducing detrimental

impacts on consumption growth once the vulnerability index exceeds this level, and this was

the case of around 58% of the surveyed households.

However, I did not find any evidence of food-price-shocks-induced poverty traps or

bifurcated welfare dynamics necessary for the existence of multiple welfare equilibria.


xx

Instead, graphical representations of the predicted consumption levels and asset indices reveal

that Ugandan households are converging towards a single welfare equilibrium located slightly

above the official poverty line, at around 29,000 Ugandan Shillings (UShs) for monthly real

values of consumption per adult equivalent and 1.10 Poverty Line Units (PLUs) for asset

index. Non-parametric (Kernel-weighted local polynomial smoothing and locally weighted

scatterplot smoother, LOWESS) and semi-parametric methods (Ruppert et al’s (2003)

penalized spline regression estimation) also indicate the absence of poverty traps caused by

exposure to food price shocks.

When households are disaggregated into different sub-groups sharing some similarities, the

econometric results suggest that different household groups appear to be moving towards

specific welfare equilibria. For instance, households exposed to food price shocks are moving

towards a consumption threshold that is 6.5% lower than the equilibrium of their unexposed

counterparts, with 30,260UShs of consumption values against 32,360UShs. Households

located below the vulnerability threshold 1.364 (meaning less vulnerable households) are

expected to reach a welfare equilibrium that is on average 57.1% greater than that of

households beyond the estimated critical vulnerability index. Hence, although there is no

evidence of food-price-shocks-induced poverty traps, the essay finds evidence of conditional

convergence across groups of households with female-educated, less educated, highly

exposed and vulnerable households to food price shocks converging towards lower

consumption and asset equilibria, regardless of the selected econometric method.

1

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2

Essay I

Food Price Volatility in Uganda:

Trends, Drivers, and Spillover Effects

1.1 Introduction

The recent unprecedented shifts in global commodity prices observed between 2007 and the

middle of 2008 and from 2010 to 2011 have revived interest and widespread concerns about

their potential adverse consequences on households, especially in developing countries.

Indeed, between 2005 and 2007, international prices of many staple foods rose drastically:

milk powder by 90 percent, maize by 80 percent, wheat by 70 percent, and rice by 20 percent

(Ivanic and Martin, 2008). Further, at the peaks of the crisis in mid-2008, the international

prices of some food commodities - such as wheat, maize, and rice - had more than doubled

(von Braun, 2008). While in developed countries the budget shares of food expenditures are

relatively modest, in developing countries, most households not only are producers and

consumers of food, but also consume all or part of the output of their productive activities.

In Uganda for example, agriculture provides about 42% of earning sources (UBoS, 2010),

employs 65% of the total labor force of the country (World Bank, 2013) and the population

relies primarily on staple foods as its main source of caloric intakes. To grasp the importance

of the staples for the population, table 1.1 gives an overview of caloric intake and

consumption of the most important staple foods in Uganda (matooke1, cassava, maize, sweet

and Irish potatoes, beans, rice, sorghum, millet, wheat, and groundnuts) between 2000 and

2011. Overall, matooke has been both the most consumed staple food with a per capita annual

average of 154kg and the most contributing item in terms of caloric intake, averaging 16.33%

throughout the sample period. Cassava, maize, and sweet potatoes also play an important role

in both consumption and daily caloric intakes. They account respectively for 12.6, 11.6 and

8.8% of average caloric intakes. The remaining staples only contribute marginally to annual

1 Matooke refers to starchy bananas that are cooked and consumed as staple (Haggblade and Dewina, 2010)


3

consumption and daily caloric intakes, revealing a diet highly diversified among the

population with no staple food accounting for more than 20% of the daily caloric intakes.

In such an environment characterized by a high dependency of the population on staple foods

for both consumption, caloric intakes and agricultural revenues, any substantial changes in

food prices (both in levels and volatility) are likely to impact on household real income,

particularly for agricultural households, and exacerbate food insecurity of the poor (Apergis

and Rezitis, 2011). A visual inspection of the price volatility of these staple foods helps

understand the need of investigating their behavior and identifying their main drivers.

Table 1.1 Caloric intakes and consumption of main staple foods (2000 – 2011)

Staple foods Caloric intakes (kcal/person/day) Consumption (kg/person/year)

Average % min max Average Min Max

Matooke 375.75 16.33 318 439 154.06 130.3 180.2

Cassava 290.25 12.62 267 312 97.24 88.8 104.7

Maize 265.25 11.55 203 344 29.05 22.4 40.7

Sweet potatoes 202.67 8.81 162 225 77.16 61.8 85.6

Beans 124.58 5.51 91 166 13.42 9.8 17.9

Millet 94.17 4.08 39 127 14.82 5.4 18

Wheat 67.67 2.94 16 97 9.01 2 13.1

Groundnuts 55.08 2.39 49 69 3.65 2.8 4.6

Rice 45.25 1.97 34 54 4.64 3.5 5.6

Sorghum 41.25 1.79 30 50 4.96 3.5 5.8

Irish Potatoes 27.75 1.21 26 29 14.27 13.4 14.9

Others 670.33 29.16 569 749

Total 2,299.83 100 2,250 2,380

Source: FAO data, various years.

Indeed, the trend of monthly real food prices in Uganda between January 2000 and December

2012 suggests that price volatility (measured by the standard deviation of real price returns)

has been time-varying over periods of both months and years and can be characterized by

three main stylized features (Figure 1.1). Firstly, it has remained relatively low between

January 2000 and December 2007, barely reaching 10 percent and averaging 7.8 percent.

Secondly, food price volatility appeared particularly high during the sub-period January 2008

and December 2012, which coincides with the recent international food price turmoil. Finally,

price volatility has peaked three times between January 2008 and December 2012: during the

second quarter of 2008, the first quarter of 2009 and the last quarter of 2011, with respectively

13, 16, and 19 percent.

Essay I

4

Figure 1.1 Monthly real food price volatility, January 2000 – December 2012

Understanding factors that drive changes in food price volatility is of utter importance for

both market participants and policy-makers. On the one hand, increases in food prices (both in

mean and volatility) imply that farmers receive high but more instable revenues from food

markets and that consumers not only have to pay consistently high prices but also cannot

perfectly predict future market prices due to their highly unpredictable variability. On the

other hand, high price volatility may be source of social tensions and conflicts, and may

hamper the efficacy of policy responses2.

There exists a rich body of literature that has investigated the determinants of food price

volatility. Macroeconomic factors such as inflation rates, adverse weather conditions,

increasing fuel and energy prices, exchange and interest rates, yield and stock levels, have

generally been identified among the key contributing factors of changes in commodity price

volatility (Pindyck and Rotemberg, 1990; Ai et al., 2006; Balcombe, 2009; Roache, 2010;

2 For example, Berazneva and Lee (2013) found that between 2006 and 2008, food riots occurred in at least 14

African countries: Guinea, Mauritania, Morocco, Senegal, Cameroon, Mozambique, Burkina Faso, Cote d’Ivoire, Ethiopia, Egypt, Madagascar, Somalia, Tunisia, and Zimbabwe. Bellemare (2015) is another example of recent studies on the impact of high prices (both price levels and price volatility) on social unrest.

Note: Weighted index of 10 key food commodities in Uganda: matooke, cassava, maize grains and

flour, sweet potatoes, beans, millet flour, rice, sorghum, and groundnuts. Nominal prices were

deflated using the UBoS all items’ consumer price index (2005/06=100).


5

Dong et al., 2011; Apergis and Rezitis, 2011; Karali and Power, 2013). Notwithstanding the

vast number of theoretical and empirical studies on commodity volatility, they have

overwhelmingly focused on spot and futures markets in developed or at least in some

emerging countries. By contrast, in developing countries and especially in Sub-Saharan

Africa, although different factors have been listed as potential causes of agricultural price

volatility, existing studies only present a qualitative, rather than a quantitative, evaluation of

these factors and are therefore unable to identify the specific contribution of each factor to

observed or historical price volatility (FAO, 2009; FAO, 2011; Minot, 2012; Gouel, 2013).

The aim of this first study is to fill this empirical gap with a twofold objective. Firstly, the

paper models conditional price volatility of the main staple foods in Uganda and examines the

extent to which volatility in principal food markets in Uganda spills over each other. This is

particularly important in the Ugandan setting insofar as previous studies (see, Rashid, 2004;

Conforti, 2004; and Boysen, 2009)3 have shown that different food markets across the country

are rather integrated. The evidence of spillover effects across food markets would therefore

imply that price stabilization policies should primarily focus more on global solutions instead

of favoring market-specific measures. Furthermore, the study addresses the question of

asymmetric effects in price volatility. Although largely analyzed in regards to financial

markets where good and bad news of the same magnitude generally have different effects,

recent studies have also found evidence of such asymmetric effects in agricultural markets

(Carpantier, 2010; Piot-Lepetit, 2011).

Secondly, the present study investigates the differential impacts of various factors in driving

changes in food price volatility in Uganda between 2000 and 2012. More specifically, the

paper aims at answering the following question: How does agricultural price volatility react to

changes in macroeconomic fundamentals and environmental factors, on the one hand, and to

own- and cross-price shocks, on the other?

3 For example, Rachid (2004) analyzes internal integration of Ugandan maize markets in the years following the

agricultural market liberalization in the early 1990’s. Using weekly wholesale price data for 8 district markets over the periods from 1993, week 1 to 1994, week 40 and from 1999, week 40 to 2001, week 30, he finds that the majority of the district markets are integrated and that integration with Kampala improved from the first to the second period.

Essay I

6

The Generalized Autoregressive Conditional Heteroscedastic (GARCH) family models are

employed to investigate both the conditional price volatility and the presence of asymmetric

or leverage effects in food price volatilities. The Vector Autoregressive (VAR) models are

used to explore the extent of spillover effects in food markets across the country and to

identify the responsiveness of food price volatilities when shocks occur in their own markets

or in others. Finally, the Seemingly Unrelated Regression (SUR) model is applied to estimate

the impact of macroeconomic variables and seasonality factors on observed food price

volatilities. The analysis is conducted for six key staple foods consumed by Ugandan

households between January 2000 and December 2012, namely matooke, cassava, maize,

sweet potatoes, beans, and millet flour.

This study, including the preceding introduction, has five sections. The foregoing has

highlighted the importance of understanding price volatility in countries largely dependent on

food consumption. In the next section, I provide a graphical overview of the patterns of food

price indices between 1997 and 2012. In section 3, I present different econometric models for

analyzing successively conditional price volatility, asymmetric and leverage effects in food

price volatilities, spillover effects across commodity markets, and factors driving the observed

or historical price volatility. Section 4 describes the data and constructs volatility variables.

Section 5 presents and discusses the results of the GARCH, VAR, and SUR models. Finally,

Section 6 concludes the paper and discusses the policy implications of the key findings.

1.2 Patterns of food price indices in Uganda

In this paragraph, I analyze the evolution of monthly consumer price indices in Uganda

between July 1997 and December 2012 and identify their main patterns. As shown in figure

1.2, while non-food price indices4 were continuously increasing, the monthly price indices of

food commodities reveal four different patterns in their evolution between July 1997 and

December 2012.

4 Here, non-food price indices represent the weighted average of six commodity groups: clothing and footwear;

rent, fuel, and utilities; household and personal goods; transport and communication; education; and health and other commodities.


7

Figure 1.2 Monthly consumer price indices, July 1997 – December 2012 (Base: 2005/06=100)

Source: Own computation based on UBoS data, various years

First phase: Stability of food price indices (July 1997 – September 2007)

During this phase, the food price index is remarkably stable, around the 2005/06 level. At the

macroeconomic level, the Ugandan government has launched substantial economic reforms

that contributed to sustaining the economic growth (6.7% on average between 1997 and 2007)

and to stabilizing the economy. Indeed, in 1999, the government introduced Poverty

Reduction Strategic Papers (PRSPs) with the aim of making the economic performance more

pro-poor. The liberalization of the economy during that period improved the incentive of the

private sector to invest into the economy which boosted the private capital formation at the

expense of public investments5. Other reforms included the Medium-Term Competitive

Strategy for the Private Sector (MTCS) in 2000 aiming at improving the performances of the

private sector6; the Plan for the Modernization of Agriculture (PMA) in 1997 whose objective

was to eradicate poverty through competitive and sustainable agriculture and agri-business

5 For example, the share of private capital formation rose from 7% of GDP in 1989/90 to 13% in 1998/9,

whereas the public capital formation fell from 7 to 5% during the same period (Devarajan et al., 2001). 6 Among its objectives, it tried to enforce prudential requirements in the banking system and carry out

supervision of the financial sector, to reduce the incidence of corruption and improve the general investment climate.

Essay I

8

sector; and the Strategic Export Intervention Program (SEIP) whose primary interest was to

increase the competitiveness of Ugandan exports. Consequently, the overall inflation rate was

very low during this period, around 5% while it reached 16.6% on average in the early 1990s.

The growth rate of the monthly food consumer price indices was relatively stable during this

period as visualized in figure 1.3.

Figure 1.3 Growth rates of monthly consumer food price indices (July 1997 – September 2007)

Source: Own computation based on UBoS data, various years

Second phase: Steep increase of food price indices (October 2007 – September 2009)

This period covers the international food price crisis of 2007/2008. Uganda food price indices

were continuously increasing with an average monthly growth rate of 2.3% against -0.005%

during the previous period. This observed pattern led several authors to analyze the potential

links between the world and Ugandan food prices and they generally came up with the

conclusion that, although the world and Ugandan domestic markets were integrated, the price

transmission was not only imperfect but also highly dependent of the type of commodities

analyzed.


9

For example, Conforti (2004) and Boysen (2009) analyzed how an increase in food prices

impacts on poverty in Uganda. Although they focused on different items in their respective

studies7, they both found that world and Ugandan domestic markets were integrated. The

same results were obtained by Rapsomanikis et al. (2003), Dorosh et al. (2003) and Bussolo et

al. (2007) who restricted their study to the analysis of the Ugandan coffee markets over

various periods and found a significant link between the world and Ugandan coffee markets.

Kaspersen and Føyn (2010) analyzed the impact of the world prices’ increases on the

Ugandan domestic markets of Robusta coffee and sorghum. They used wholesale weekly

prices of Foodnet, collected at the main local markets in four districts (Gulu, Jinja, Mbale and

Soroti). Contrarily to previous studies, their paper found that sorghum markets in Uganda,

unlike the Robusta coffee’s markets, were not integrated into the world markets. Their

empirical analysis also indicated that rising food prices (of little-traded crops) in world

markets would not have a direct effect on food prices in Uganda. Finally, Benson et al. (2008)

assessed the potential impact of rising world food prices in 2007/2008 on the welfare of

Ugandan households. They suggested that only domestic prices of internationally traded

goods (in their study, rice and wheat) were directly affected by international market prices.

By and large, these studies suggest that international food prices were imperfectly transmitted

to Ugandan local markets and among the reasons usually put forward, we have high

transaction costs due to the insulation of the country from international markets (Benson et

al., 2008) and the relatively large quantity and range of staples consumed from home

production (Boysen, 2009). Therefore, the observed increases in Ugandan food prices during

this period have been attributed, without formal tests of the proposed explanations, to diverse

factors, including the global rise in oil prices, the post-election crisis in Kenya at the

beginning of 2008 that has increased the demand for Ugandan products, new demands from

DR Congo and southern Sudan, and localized production problems, for example floods in the

Teso region between July and October 2007 (Benson et al., 2008).

Third phase: Sharp decline in food price indices (October 2009 – June 2010)

Between October 2009 and June 2010, food inflation ceased off its upward trend

characterizing the previous spell but still remained higher than during the period July 1997 -

7 Wheat, sorghum, milk powder, sorghum, maize, rice, cassava, soybean, poultry and pork meat for Conforti

and matooke, cassava flour, millet flour, cassava fresh, sweet potatoes, rice, dried beans Nambale, dried beans Kanyebwa, Irish potatoes, maize flour and “unpounded” groundnuts for Boysen.

Essay I

10

September 2007. Among the potential causes of this food price deflation, we may find the

combined effects of good harvest periods in major cereals (especially, maize and rice) and

relatively lower fuel prices. With regards to rainfall variability, this period which covers

almost all the four agricultural seasons8 in Uganda enjoyed particularly good average rainfall

levels. Indeed, from figure 1.4, it appears that rainfall levels between January and June 2010

were globally higher than the corresponding months of 2007, 2008, and 2009 which led to

relatively important production during the first harvest season.

Figure 1.4 Average rainfall levels (in mm) in Uganda (2007 – 2010)

Source: Sector economic performance reports of the Ministry of Energy and Mineral Development of

Uganda, various years.

On the other hand, although rainfall was lower in October and November 2009 comparatively

to other years, it started increasing since December 2009 with an impact on the production

during the second harvest period.

8 The second planting season, which usually starts from September and goes until November, the second

harvest period which covers the period December to February, the first planting season over the months of March to May, and the first month of the first harvest period (Asiimwe and Mpuga, 2007).


11

Furthermore, fuel prices could have played an important role in explaining the downward

trend in food price indices. Indeed, many Ugandan farmers are located in remote areas, far

from the main roads of the country. Access to food and input markets therefore requires

relatively important transport costs that may be detrimental for small farmers and increase

food prices charged by producers due to higher production costs. Fuel price inflation as

depicted in figure 1.5 remained high in 2008 (around 10% quarterly) but sharply decreased

between January 2009 and June 2010. During this period, the average quarterly fuel inflation

was -3.75% against 8.1% between September 2007 and June 2009.

Figure 1.5 Evolution of quarterly fuel pump inflation in Uganda, September 2007 – September 2010

Source: Bank of Uganda’s Quarterly macroeconomic reports, various years.

Fourth phase: Skyrocketing food price indices (July 2010-December 2012)

During this last phase, Uganda has experienced the second remarkable increase in its food

price inflation. Indeed, food inflation, which accounts for around 27.2% in the overall

inflation, drastically increased from -2.8% in the second quarter of 2010 to 12% in the first

quarter of 2011 (Bank of Uganda, 2011). Furthermore, since April 2011, food inflation has

not stopped rising, peaking in October 2011 and April 2012, with an index of around 250.

This surge in food prices may result from various and intertwined factors.

-5

0

5

10

15

20

sept.-07 févr.-08 juil.-08 déc.-08 mai-09 oct.-09 mars-10 août-10

Fuel pump inflation (%)

Essay I

12

First, international crude oil prices accelerated since March 2011 and reached 123$ per barrel

in April 2011. Second, the rise in food crop inflation might have resulted from periods of

droughts that adversely affected agricultural production in most growing food regions of the

country. Third, increased fuel prices coincided with the depreciation of the Uganda

Shilling/US dollar exchange rate (figure 1.6). Finally, increased inflation in Uganda’s trading

partners, particularly in Kenya, Euro area, China, and the United Kingdom, may have been

translated into rising food prices. For example, in Kenya, a country that accounted for around

19% of the total Uganda exports between 2010 and 2013, the overall annual inflation rate

increased from 4% in 2010 to 14% in 2011, while in the Euro area, China, and the United

Kingdom, it rose from 1.5, 3.3, and 3.3% in 2010 to 3.3, 5.4, and 4.5% in 2011, respectively

(World Bank , 2013).

Figure 1.6 Evolution of nominal and real effective exchange rates UShs/$US (July 1997- March 2013)

1.2 Econometric models of conditional volatility, asymmetric and spillover effects,

and drivers of price volatility

In this section, different econometric models of evaluating conditional food price volatility,

testing for the presence of asymmetric and spillover effects of price volatilities across

Source: Own computation based on Bank of Uganda (2013)


13

Ugandan commodity markets, and examining the differential impact of potential drivers of

observed volatilities are successively presented.

1.2.1 Conditional volatility model

To analyze historical food price volatility in Uganda, I draw on the Autoregressive

Conditional Heteroscedastic (ARCH) model introduced by Engle (1982) and the generalized

ARCH (GARCH) model by Bollerslev (1986). The ARCH model is specified so that the

current price volatility will be positively affected by the more recently observed shocks

whereas the GARCH model assumes a positive impact of both previous shocks and

volatilities.

Consider the following general qp,ARMA process with autoregressive order p and moving

average order q:

tq

ttp LXYL

where

jttj

qq

q

pp

p

YYL

LLLL

LLLL

...1

...1

221

221

with tY , the dependent variable, is a food price volatility time-series ; jtY , j = 1, 2,…, p, its

lagged dependent variables; tX are independent variables; L is the lag operator; and t are

the error terms assumed to be white noise. The mean equation (1.1) does not take account of

heteroscedasticity of the time series process generally observed in the form of fat tails and

leverage effects (Würtz et al, 2006). To solve this problem, Engle (1982) defines the error

terms in (1.1) as an autoregressive conditional heteroscedastic process, giving the following

qARCH process:

ttY βXt

where

q

i

itit

ttt N

1

22

21 ,0

(1.1)

(1.2)

(1.3)

(1.4)

Essay I

14

with 2t is the time-varying variance of the error term t ; 1t is the information set

available at time t-1. In the qp,GARCH , the lagged values of 2t are now included into the

model which gives:

p

j

jtj

q

i

itit

1

2

1

22

where

is the mean of 2t ; i and j are the ARCH and GARCH terms, respectively.

For the qp,GARCH to be stationary, the following restrictions are sufficient:

jiji

p

j

j

q

i

i

,,0,,0,1

11

I introduce two types of variables in the mean equation (1.3). First, to check whether the

conditional price volatility has significantly changed since 2008, I include in the vector X a

dummy variable Dum which takes the value 1 during periods of structural breaks in food

price series and 0 otherwise (see next section). The sign of this variable is expected to be

positive, implying a significant increase in conditional price volatility associated with these

turning points.

Second, one of the common features of agricultural food markets is the presence of

seasonality in volatility patterns. Food prices tend to fluctuate across the agricultural season,

rising during the planting season as the stocks of commodities are depleting and declining

during the harvest period (Buguk et al., 2003). To incorporate deterministic seasonal

components into the volatility models, I follow Goodwin and Schnepf (2000) by adding a sum

of trigonometric functions corresponding to the tth

month of the year into the vector X.

Concretely, if tm represents the month of the year associated with the observation t, the

seasonal component ts can be written as:

K

k

tk

tkt

mkmks

112

2sin

12

2cos

where k and k , Kk ,...,1 , are parameters to be estimated.

Through this specification, the unknown seasonal function is expressed as a kth

-order Fourier

approximation within a period of one year. The presence of seasonal patterns into price

(1.5)

(1.6)

(1.7)


15

volatility can then be assessed by testing the significance of the estimated values of k and

.k Following Goodwin and Schnepf (2000) and Buguk et al. (2003), k = 3 is used in

deriving the seasonal component.

1.2.2 Asymmetric and leverage effects

One of the limitations of a standard GARCH (1, 1) model is its assumption of symmetric

impacts of good and bad news on volatility. However, empirical evidence, originated from

financial markets and stock exchange, extensively shows that not only is there an asymmetric

response of price volatility to positive and negative past returns (asymmetric effects) but also

increases in volatility appear to be larger when previous returns were negative than when they

were positive with the same magnitude (leverage effects) (Black, 1976; French et al., 1987;

Nelson, 1991a, b; Engle and Ng, 1993; Villar, 2010; Apergis and Rezitis, 2011). In terms of

food prices, this would mean that households would not react identically to unanticipated

increases and decreases in food prices of the same magnitude. To test for the robustness of the

GARCH (1, 1) estimation results, I now allow price volatility to react asymmetrically to both

positive and negative shocks. To that end, I estimate an Exponential GARCH model proposed

by Nelson (1991b)9. In addition to accounting for asymmetry in the responsiveness of food

price volatility to shocks of opposite signs, the EGARCH model does not impose any

restrictions on the parameters to guarantee a positive variance as do standard GARCH models

(Villar, 2010). The EGARCH (1, 1) model specifies the conditional variance 2t of equation

(1.5) as follows:

21

1

1

1

12 ln2

ln

t

t

t

t

tt

where the ratio ttth / represents the standardized shock for time t. The parameters and

capture the presence of asymmetric and leverage effects in food price volatility whereas

reports persistence in volatility. Since the EGARCH (1, 1) model is based on the standardized

residuals th , the regularity condition is satisfied if 1 .

The model will be symmetric if 0 and in that case the model reverts to the standard

GARCH (1, 1). It will exhibit asymmetric effects if is statistically significant. When 0

9 Other possibilities include Asymmetric power ARCH (A-PARCH) models first proposed by Ding et al. (1993) or

Threshold ARCH (TARCH) models of Zakoian (1994).

(1.8)

Essay I

16

and significant, then there exist leverage effects, meaning that negative shocks on price

volatility have larger impact than positive shocks of the same magnitude. The effects of high-

(unexpected price increases) and low-price news (unexpected price decreases) on the

conditional variance will be given respectively by and (Zheng et al., 2008). If

, then low-price news have more effects on the conditional variance than high-

price news of the same magnitude.

1.2.3 Volatility spillover model

To examine the possibility of spillover effects from one market to another within the country,

I specify a multivariate framework in which the current price volatility of a commodity i is

allowed to depend on both past own shocks and price shocks to other commodities. To that

end, I use a Vector AutoRegressive (VAR) specification of Sims (1982) which identifies how

each endogenous variable (i.e. food price volatility) reacts over time to own shocks and to

shocks from other food markets. I estimate the following VAR model:

t

t

p

k

iktk

p

k

iktk

p

k

iktk

p

k

iktk

p

k

k

p

k

k

k

k

it

it

u

U

Yd

YD

Yc

YC

qb

QB

a

A

Y

Y

1

1

1

1

1

1

where itY is the price volatility of commodity i and i

tY is a vector of price volatilities of other

commodities which effects are assumed to spill over the market of the commodity i ; Q is a

vector of dummy variables capturing structural breaks; kA , kB , kC , and kD and their

lowercase counterparts are the vector of coefficients in i

tY and i

tY equations, respectively.

Schwartz information criterion was used to select the appropriate lag length.

1.2.4 Model of drivers of food price volatility

One of the questions arising when inspecting figure 1.1 is whether the blame of the upward

trend in food price volatility in Uganda could be put on the international food price turmoil of

2007/8. The answer depends crucially on how integrated are Ugandan domestic markets to

global commodity markets. By and large, the existing studies tackling this issue have come up

with the conclusion that international food prices were imperfectly transmitted to Ugandan

local markets. As previously outlined, high transaction costs due to the insulation of Uganda

(1.9)


17

from international markets (Benson et al., 2008; Kaspersen and Føyn, 2010) and the relatively

large quantity and range of staple foods consumed from home production (Boysen, 2009) are

the reasons usually advanced to explain these results. Here, I take a more formal approach by

identifying and analyzing the differential contributions of the key drivers to the observed

price upswings in the main Ugandan markets.

Economic theory predicts that changes in price volatility will depend to a larger extent on

factors directly affecting the decisions of buyers and sellers of commodities analyzed and to a

smaller extent on indirect factors. Direct determinants will generally include supply shocks

(such as weather variability, changes in input prices, yield variability, and changes in stock

levels) and demand shocks (like changes in income or consumption habit persistence)

whereas indirect causes may result from speculative behavior, volatility in market prices of

substitute or complement commodities, exchange rate volatility, or inflation rates.

The choice of the potential determinants of food price volatility is mainly guided here by

economic theory, results of other empirical studies, and data availability constraints. To

analyze the impact of macroeconomic and environmental variables on changes in price

volatility, I estimate the Seemingly Unrelated Regression (SUR) model introduced by Zellner

(1962):

6,...,1;122012,...,12000

,221 ,

$/,,

immM

PlantinglHarvestkHarvesth

RFVfIRVeFPVdERVcCPIbaCPV

Miiii

MiMiMiShsMiMiiMi

where MiCPV , is the food price volatility of the commodity i in month M; ia , ib , ic , id , ie

if , ,ih ,ik il are parameters to be estimated; Mi, are the error terms.

Among the explanatory variables, I include the inflation rate volatility MCPI , real effective

exchange rate volatility between the Uganda Shilling and the US dollar $/,ShsMERV , fuel price

volatility MFPV , interest rate volatility MIRV , and rainfall variability MRFV as well as dummy

variables for different agricultural seasons in the country Harvest1, Harverst2, and Planting2.

The variable MCPI captures the impact of the overall food inflation on the price movements

of a particular commodity. I expect a positive correlation between the changes in consumer

price index and individual price volatility (Roache, 2010; Azad et al., 2012).

(1.10)

Essay I

18

Volatility in the exchange rates increases the riskiness of both the returns of the exporters and

the prices of imported goods. Including this variable into the model will help discriminate the

effects of regional and international forces on domestic price variations of each commodity

(Gilbert, 1989; IMF, 2008). I adopt a standard measure of exchange rate volatility $/,ShsMERV

of a particular month M by taking the standard deviation of the percent changes of the real

effective exchange rate MRE between the Uganda Shilling and the US dollar over a three-

month window width (Chowdhury 1993; Hau, 1999; Arezki et al., 2012)10

:

2

1

3

1

221 )ln(ln

3

1

i

iMiMM REREERV

The effective exchange rate is computed in such a way that a decline of its value implies a

real appreciation of the domestic currency. I assume that the impact will be higher and

significantly positive for commodities which are more regionally and/or internationally traded

by Uganda, such as maize, millet flour, and beans.

The rainfall volatility variable MRFV captures the impact of weather shocks on price

volatility. Weather variability is among the main causes of production shortfalls, particularly

in developing countries where agricultural plots are predominately rain-fed. As suggested by

the storage model, supply shocks (here consecutive to weather shocks) are likely to be

important factors of agricultural price volatility (Deaton and Laroque, 1992, 1996). I

hypothesize that the more rainfall-dependent the commodity, the larger the impact of weather

variability on its price instability.

Interest rate volatility MIRV is used as a proxy for commodity stocks given the absence of

monthly data. It therefore represents the opportunity costs of holding potential commodity

stocks (Balcombe, 2009; Azad et al., 2012; Karali and Power, 2013).

Transaction costs and particularly transportation costs are also obvious candidates as drivers

of food price volatility in Uganda. Fuel price volatility MFPV is used as proxy of these costs.

Indeed, farmers often have to choose between selling their products at the farm gate and

therefore earn less or carrying these products to markets and incur a transport cost (Fafchamps

and Hill, 2005). When a crop has a low value-weight ratio (such as matooke or cassava), these

10

I also used other alternatives window widths (1, 4, and 6 months) to check for the robustness of the volatility measures but results did not significantly change.

(1.11)


19

costs may represent a non-negligible component of the market prices and fuel their volatility.

It is thus hypothesized that the impact of fuel price volatility will be more important the

heavier the commodity. Similarly to the exchange rate volatility, I measure inflation rate,

interest rate, rainfall and fuel price volatilities as the standard deviation of their growth rate

with a three-month window width.

Finally, it is likely that food prices exhibit important seasonalities, being relatively higher and

lower during planting and harvest seasons, respectively (Koekebakker and Lien, 2004). To

account for that possibility, I include seasonal dummy variables corresponding to different

harvest and planting seasons in Uganda: Harvest1 takes 1 if the corresponding months are

June, July and August, and 0 otherwise; Harvest2 has 1 if months are December, January and

February, and 0 otherwise; and Planting2 takes 1 if the corresponding months are September,

October and November, and 0 otherwise. The first planting season (March, April, and May)

has been used as baseline.

1.3 Data

In all the estimated models, the dependent variables are the food price volatilities. There exist

different ways of measuring historic food price volatility. For example, O’Connor and Keane

(2011) and Piot-Lepetit (2011) used the coefficient of variation (CV) which is the ratio of the

standard deviation over the mean. However, as pointed out by Minot (2012), given the non-

stationarity in most food prices, the estimates of price variability derived from the standard

deviation approach are dependent on the sample size and may be particularly large when the

time period approaches infinity. To avoid this undesirable feature, I follow Gilbert and

Morgan (2011) and use instead the standard deviation of price returns, where returns stand for

the proportional change in logarithm prices. Therefore, the average monthly price volatility of

the ith

commodity in the tth

month tiCPV , can be formalized as follows (Balcombe, 2009;

Minot, 2012):

N

t

titjiti rrN

CPV

1

2,,,,

1

1

where

N

t

tjititjitjitji rN

randppr

1

,,,1,,,,,,

1)ln()ln(

(1.12)

(1.13)

Essay I

20

tjip ,, and tjir ,, are respectively the real price and price return of the ith

commodity in the jth

week of the month t. tir , stands for the average monthly price return of the ith

commodity. N

represents the number of weekly price information available for each month.

I use data obtained from different sources: exchange and interest rates are obtained from Bank

of Uganda; consumer price indices, inflation rates, and rainfall data are collected from various

issues of Statistical abstracts of the Uganda Bureau of Statistics (UBoS) and the Background

to the Budget of the Ministry of Finance, Planning, and Economic Development. Fuel pump

prices are obtained from the Agriculture Market Information System (AGMIS) Uganda.

Monthly nominal food prices of the selected commodities come from time series’ prices

collected by the Foodnet market price information project of the International Institute of

Tropical Agriculture (IITA). The dataset contains weekly wholesale price series for around

twenty Ugandan markets across all the geographical regions11

and for more than 25 staple

foods from September 1999, week 40 to December 2012, week 52. For each series, nominal

prices were deflated by the UBoS all items’ consumer price index (2005/06=100) to take

account of potential changes in the purchasing power of Ugandan households.

Table 1.2 reports the values of unconditional price volatility of 6 food commodities, namely

matooke, cassava, maize, sweet potatoes, beans, and millet flour between January 2000 and

December 2012 (see Appendix A.1 for individual volatility plots). The data are divided into

two sub-periods (January 2000 to December 2007 and January 2008 to December 2012),

which gives 96 and 60 monthly observations, respectively. A standard F-test of variance

equality is presented in the penultimate column and its implications in terms of significance

rise or fall in unconditional volatility are summarized in the last column.

The table reveals that monthly food prices have been globally more volatile since January

2008, rising from 8.4 to 11.7%, which represents an average growth rate of 38.8% between

the two sub-periods. The distribution of food price volatility across commodities shows that

beans and sweet potatoes were the most volatile respectively in the first and second sub-

periods.

11

Arua, Gulu, Kitgum and Lira in the Northern region; Luwero, Masaka, Rakai, Kiboga, and Kampala (Kisenyi, Owino, Nakawa, Kalerwe) in the Central region; Iganga, Mbale, Jinja, Soroti, and Tororo in the Eastern region; and Jinja, Kabale, Kibale, Kasese, Hoima, and Mbarara in the Western region


21

Table 1.2 Unconditional price volatility of key food commodities in Uganda (2000m1 –2012m12)

2000m1-

2007m12

2008m1-

2012m12

Growth

rate

2000m1-

2012m12

F-test (p-value) Conclusion

Matooke 0.099 0.134 0.354 0.112 1.617 (0.037) Significant rise

Cassava 0.056 0.108 0.929 0.076 3.699 (0.000) Significant rise

Maize 0.101 0.127 0.257 0.111 1.757 (0.014) Significant rise

Sweet potatoes 0.097 0.154 0.588 0.120 3.171 (0.000) Significant rise

Beans 0.112 0.114 0.018 0.112 0.993 (0.989) Insignificant rise

Millet flour 0.040 0.064 0.600 0.049 3.437 (0.000) Significant rise

Average 0.084 0.117 0.388 0.065 2.714 (0.000) Significant rise

Note: The growth rate of each price volatility is defined as aab /)( , where a and b are respectively

the mean volatility during the first and the second sub-periods. Source: Analysis based on price data

from FoodNet project.

Globally, price volatility is the lowest for millet flour (4.9%) and cassava (7.6%) and the

highest for sweet potatoes (12%), matooke (11.2%), and maize (11.1%). Furthermore, all

commodities but beans have exhibited a significant increase in the variance of their

unconditional volatility since January 2008.

1.4 Empirical results

1.4.1 Conditional price volatility

Unconditional price volatility assumes that the stochastic processes generating the data on

price returns are independent and identically distributed and therefore, the data may be

considered as random draws from the same (unconditional) distribution. In the conditional

volatility model, the stochastic process has now a time-varying volatility (Green, 2012). The

model thus estimates a conditional variance at each date in the time series given current and

past price information (Gilbert and Morgan, 2011).

A prerequisite for estimating conditional volatility through GARCH models is the stationarity

of the process being analyzed. However, since our sample covers periods of recent food price

turmoil, I suspect the possibility of breaks and shifting trends in Ugandan price series. In case

of evidence in favor of structural breaks in price series, standard econometric tests

(Augmented Dickey-Fuller, Phillips-Perron, or Dickey-Fuller Generalized Least Squares)

become biased because of their potential confusion of structural breaks in the series as

Essay I

22

evidence of non-stationarity (Baum, 2005; Ghoshray et al., 2014). Hence, before performing

unit root tests, I first identify the potential breaks or turning points in food price trends,

following testing procedures proposed by Clemente, Montañés, and Reyes (1998)

(henceforth, CMR) and Bai and Perron (2003) (henceforth, BP).

Detecting structural breaks in commodity food prices

The behavior of food commodity prices depicted in previous paragraphs highlighted the

possibility of breaks and shifting trends in Ugandan price series. However, relying strictly on

visual inspection of data plots to detect the presence of structural breaks may be misleading

due to its inherent impossibility to disentangle a simple level shift from real shocks. Hence,

since Prebisch (1950) and Singer (1950), researchers such as Perron (1989), Zivot and

Andrews (1992), Vogelsang and Perron (1998), Clemente, Montañés, and Reyes (1998), Bai

and Perron (2003), Harvey et al. (2009), Perron and Yabu (2009a, b), and Ghoshray et al.

(2014) have developed various econometric procedures to detect breaks in the level and/or the

scope of commodity trends and estimate both the number and locations of break dates.

Although the primary motivation behind these studies and their methodological procedure has

been to test the Prebisch-Singer hypothesis12

, they can also be used to differentiate real

structural breaks from pure level shifts identified in the previous sections.

Clemente, Montañés, and Reyes’ model

The CMR procedure allows for up to two distinct and endogenous structural breaks using two

different models: the additive outliers model (the AO model) which identifies a sudden

change into a time series and the innovative outliers model (the IO model) that tests for a

gradual shift in the mean of the time series (Baum, 2005). The AO model is defined as

follows:

tttt vDUDUy 22110

where

k

i

k

i

titiititbi

k

i

itbit evvDTDTv

1 1

,22

1

,11

12

The Prebisch-Singer hypothesis states that the time series of primary commodity prices relative to manufactured goods present a downward trend in the long run. Theoretical explanations of such declining relative commodity prices include “…a low income elasticity of demand for primary commodities, lack of differentiation among commodity producers (…), productivity differentials between North (industrial) and South (commodity producing) countries, and asymmetric market structure (…)” Harvey et al. (2010:2)

(1.14)

(1.15)


23

In equation (1.14), yt is the commodity price (in levels or logged) at time t;

.2,1with,otherwise0andif1 iTBtDU iit

There are two potential

break points, TB1 and TB2, unknown ex ante and determined by grid search. The residuals

from (1.14), ,tv are then estimated in equation (1.15) using their lagged values, lagged

differences, and a set of dummy variables for the test tractability. In equation (1.15),

1, tbiDT for 1 iTBt

and 0 otherwise, with i = 1,2. The model is then estimated over

different feasible couples of TB1 and TB2, seeking for the minimum t-ratio for the null

hypothesis .1 Perron and Vogelsang (1992) provided critical values that will then be

compared with the value of the minimum t-ratio.

The IO model uses an ARMA representation to express the shocks affecting the price series in

the following formulation:

k

i

titittbtbttt eyvDTDTDUDUv

1

1,22,1122110

In both AO and IO models, an estimate of 1 will indicate that the price series has not a

unit root. The appropriate lag order of k is determined using sequential F-tests13

.

Bai and Perron’s model

Two important weaknesses may bias the results from the CMR model. Indeed, imposing a

predefined number of potential breakpoints (here, maximum two) to the data generating

process while in reality there are more can render the tests inefficient and either cause

spurious appearance of non-stationarity of the price series in a trend stationary process

(Perron, 1989) or incorrectly suggest stationarity in a non-stationary process (Leybourne et

al., 1998). To address this problem, Bai and Perron (2003) developed AO and IO models that

account for multiple breaks. They test the null hypothesis of absence of breakpoints vs k

breaks and k vs k + 1 breaks using an efficient algorithm to obtain the global minimisers of

the sum of the squared residuals. Their dynamic programming algorithm allows, on the one

hand, for both pure and partial structural changes, where all (respectively some) coefficients

13

Stata routines clemao2 and clemio2 implement the AO and IO models of CMR procedure for two breakpoints, respectively.

(1.16)

Essay I

24

are subject to changes, and on the other, the construction of confidence intervals of

breakdates14

.

In both the CMR and BP models, I apply the following procedure. First, I test for one

structural break in the slope of the trend function while allowing for the intercept to change.

Second, given the evidence in favor of one structural change in a time series, I then test for

one against two or more break points in the data. I choose between the AO and IO models for

each food commodity based on the value of the minimum t-statistics of dummy variables

introduced in the models. Specifically to the BP test, I select the optimal number of break

dates that minimizes the Bayesian Information Criteria.

Table 1.3 reports the results for the 6 food price series using the Clemente, Montañés, and

Reyes (1998) and Bai and Perron’s (2003) models for endogenously determined break points

in each price series.

Table 1.3 Optimal endogenous break dates of food price series in Uganda

Commodity Clemente et al. (1998) Bai and Perron (2003)

One break Two breaks One break Two breaks

k TB1 k TB1 TB2 TB1 TB1 TB2

Food*

- - 2 2008m8 2011m5 - 2008m5 2008m8

Matooke*

- - 1 2005m1 2008m3 - 2008m3 2011m1

Cassava*

- - 2 2008m7 2009m8 - 2008m10 2011m1

Maize*

3 2008m3 - - - - 2008m3 2011m3

Sweetpotato**

- - 1 2008m2 2009m9 - 2008m4 2009m1

Beans**

3 2007m10 - - - - 2007m10 2011m2

Millet flour**

4 2009m2 - - - 2009m7 - -

Note: * and ** mean that the AO or IO models have been applied in the CMP and BP procedures, respectively.

The results from table 1.3 show that all selected commodities contained either one or two

breaks in the slope. Out of the 6 food commodities, respectively 1 and 3 commodities were

found to exhibit one structural change in the BP and CMR models. A number of interesting

features can be derived from these results.

14

Zeileis et al. (2003) developed the package strucchange in the R system that performed all tests developed in Bai and Perron (2003).


25

First, the AO model was more efficient in explaining the price behavior of matooke, cassava,

and maize which reveals that breaks in the scope of these series took place rapidly rather than

gradually. Second, both CMR and BP models detect similar break points for 2 commodities –

matooke and beans– and for the consumer food price index. Hence, December 2007 and

March 2008 were selected as optimal endogenous break dates by both models for beans,

matooke, and maize, respectively. In December 2007, monthly real prices of beans exceeded

for the first time 1,000UShs, growing by 11.5% from the previous month while since March

2008, matooke prices have consistently been above 400UShs.

Third, discrepancies between the break points identified by both models are more or less

important depending on each commodity. Indeed, while the CMR model selects January 2005

and March 2008 as optimal dates of matooke, the BP model instead started with March 2008

as first break point and January 2011 as the second one. Furthermore, CMR model only

identified one break point in the case of maize and beans against two break dates in BP’s.

However, as stated above, the BP model is more robust in case of conflicting results with the

CMR since it does not impose any limit to the number of potential breaks which can be

selected a posteriori using either the BIC or RSS criteria (Ghorshay et al., 2014).

To sum up, despite discrepancies between CMR and BP models, a general conclusion

emerging from the above analysis is that key commodity food prices in Uganda have been

characterized by shifting trends since 2008. In fact, the estimated break dates have globally

occurred when significant internal, regional, and international events took place in food

commodity markets. An important number of break dates were observed in the first and last

quarters of both 2008 and 2009 as well as the first semester of 2011.

Unit root tests

Given evidence of structural breaks in all price series, I perform Bai-Perron’s unit root tests

(table 1.4). It appears that even when accounting for the presence of structural breaks in the

time series, all the prices are difference stationary I(1) variables. I then apply the Box-Jenkins

methodology to determine the values of p and q in the ARMA (p,q) process through the

Bayesian information criteria (BIC).

Essay I

26

Table 1.4 Bai-Perron’s unit root tests in the presence of structural breaks in food prices

Commodities TB1 ; TB2 supF-stat Conclusion

Matooke 2008M3 ; 2011M1 3.049 I(1)

Cassava 2008M10 ; 2011M1 2.046 I(1)

Maize 2008M3 ; 2011M3 4.758 I(1)

Sweetpotato 2008M4 ; 2009M1 8.042 I(1)

Beans 2007M10 ; 2011M2 7.805 I(1)

Millet flour 2009M7 3.435 I(1)

Food price index 2008M5 ; 2008M8 5.716 I(1)

Note: The critical values for 15% trim, 5% significant levels, and 1 regressor (each commodity price)

are 8.58 and 7.22 for one and two break dates, respectively (Bai and Perron, 2003).

GARCH (1, 1) estimation results

Table 1.5 shows the GARCH (1, 1) estimation results with structural breaks and seasonality in

price volatility. Since the turning points occurred during the first quarters of 2008 and 2011

for most commodities, the Dum variable takes 1 for those months and 0 otherwise. All

ARCH coefficients ( ) are significant at 10% level and positive, thereby satisfying the

necessary and sufficient conditions for the validity of the ARCH specifications. Furthermore,

the GARCH (1, 1) estimated coefficients for all the commodities satisfy the covariance

stationary condition since 1 for each staple food. The sum of the ARCH and GARCH

terms helps analyze the persistent nature of shocks to food price volatility. The closer the sum

of these terms to one, the more persistent the shocks to food price volatility. The results reveal

that shocks are more persistent for most commodities, suggesting that once a shock occurs,

price volatility tends to persist for a long period (Apergis and Rezitis, 2011), particularly for

matooke, cassava, and beans.

With regards to the impact of structural breaks on estimated conditional price volatility, the

empirical results (coefficients of the variable Dum ) indicate that, at a 1% significance level,

the mean of the conditional volatility has increased for half of the commodities analyzed,

namely cassava, sweet potatoes, and millet flour. As shown in table 1.2, these commodities

were characterized by the most important growth rates in their unconditional price volatility.

Moreover, they are generally traded regionally which, as predicted by trade or spatial

equilibrium models, implies that their prices would be more sensitive than others to breaks or

shifting trends associated with internal or regional market events.


27

The presence of deterministic seasonal components in price volatility can be analyzed through

the estimated trigonometric seasonality terms k and k . For each commodity, only around

half of the seasonal components are statistically significant, suggesting a relatively moderate

seasonality effect on conditional mean volatility.

Table 1.5 Results of the GARCH (1, 1) model estimation

Matooke Cassava Maize

Sweet

potatoes

Beans Millet

flour

Mean equation :t

t DumY

33221133

2211

sinsinsincos

coscosconstant

Constant 0.002

(0.006)

0.002

(0.003)

0.002

(0.006)

0.004

(0.007)

0.005

(0.008)

0.003

(0.003)

Dum

0.012

(0.042)

0.038

(0.014)***

0.011

(0.036)

0.106

(0.030)***

-0.040

(0.073)

0.017

(0.007)**

1 0.004

(0.002)**

-0.002

(0.005)

-0.005

(0.007)

-0.010

(0.010)

-0.001

(0.009)

-0.002

(0.001)**

2 0.002

(0.009)

-0.007

(0.004)**

0.005

(0.003)*

0.021

(0.010)**

-0.020

(0.009)**

-0.001

(0.000)**

3 0.004

(0.001)***

-0.007

(0.005)

-0.010

(0.008)

-0.007

(0.011)

0.004

(0.002)**

-0.000

(0.000)*

1 0.004

(0.007)

0.001

(0.000)***

0.003

(0.001)**

0.007

(0.004)**

0.004

(0.010)

-0.000

(0.003)

2 0.002

(0.007)

0.002

(0.005)

-0.009

(0.005)**

-0.008

(0.010)

-0.005

(0.009)

0.001

(0.000)**

3 0.017

(0.009)*

0.001

(0.000)***

0.002

(0.008)

0.010

(0.004)**

0.026

(0.009)***

0.004

(0.004)

Variance equation: 21

21

2 ttt

0.001

(0.001)

0.001

(0.000)**

0.002

(0.001)**

0.003

(0.001)**

0.014

(0.001)***

0.001

(0.000)**

0.155

(0.088)*

0.214

(0.111)*

0.339

(0.194)*

0.269

(0.163)*

0.033

(0.017)*

0.290

(0.162)*

0.761

(0.131)***

0.769

(0.219)***

0.463

(0.100)***

0.496

(0.219)**

0.871

(0.027)***

0.559

(0.264)**

0.916 0.983 0.802 0.765 0.904 0.849

Note: Standard errors are given into brackets with ***

, **

, and *

denoting significance at 1, 5, and 10%

levels, respectively. tY is the food price volatility in month t. is the GARCH term, is the ARCH

term. 12/2coscos tk mk and 12/2sinsin tk mk , .3,2,1k

Essay I

28

Indeed, when we look, for example, at the patterns of price volatility for each agricultural

season in Uganda (see Appendix A.2), there is no clear picture of whether price volatilities

were higher during planting seasons as one would expect. The last row of the Appendix A.2

reveals that for some commodities, the average monthly volatility was higher during planting

seasons (the case of cassava and beans) while for others harvest periods were associated with

greater volatility (for example matooke and maize). This lack of strong seasonality in price

volatility has also been found by Buguk et al. (2003) and Balcombe (2009).

1.4.2 Asymmetric and leverage effects in food price volatility

Table 1.6 summarizes the estimated results of the EGARCH (1, 1) model for each food

commodity. The Lagrange Multiplier (LM) statistic for a joint test for the significance of

ARCH/GARCH effects (parameters ,, and ) is also provided. The effects of high-

(unexpected price increases) and low-price news (unexpected price decreases) on the

conditional variance as well as the existence of the leverage effects are shown in the last three

rows of the table.

Table 1.6 EGARCH (1, 1) estimation results, Monthly data, 2000 – 2012

Parameters Matooke Cassava Maize Sweet

potatoes

Beans Millet flour

-8.125

(1.191)***

-2.872

(0.895)***

-2.245

(0.951)**

-0.600

(0.179)***

-1.071

(0.256)***

-2.288

(1.093)**

0.122

(0.084)

-0.038

(0.141)

0.065

(0.152)

0.719

(0.173)***

-0.970

(0.202)***

0.260

(0.151)*

0.311

(0.163)*

1.103

(0.212)***

0.696

(0.238)***

0.315

(0.105)**

0.605

(0.157)***

0.600

(0.273)**

-0.556

(0.229)**

0.510

(0.152)***

0.615

(0.166)***

0.865

(0.046)***

0.773

(0.058)***

0.661

(0.161)***

LM stat 22.47***

51.91***

35.63***

70.72***

77.06***

70.84***

0.433 1.065 0.761 1.034**

-0.365***

0.860**

0.189 1.141 0.631 -0.404**

1.378***

0.340**

Leverage

effect?

No No No Inverse Standard Inverse

Note: Standard errors into brackets with ***

, **

, and *denoting significance at 1, 5, and 10%,

respectively. The Lagrange Multiplier statistic computed under the null hypothesis that , , and

are jointly zero.


29

Interesting features are highlighted in table 1.6. First, it reveals that price volatility reacts

symmetrically to positive and negative past shocks for half of the commodities under

investigation, matooke, cassava, and maize, but asymmetrically to positive and negative

shocks for sweet potatoes, beans, and millet flour. Second, the estimated value of is

statistically significant for all food commodities which indicates that the absolute size of past

shocks affects current food price volatility. The effects were the largest for cassava and maize

with respectively 1.10% and 0.70% increases of current price volatility due to past shocks.

Third, once asymmetric effects of innovations or shocks are accounted for, only beans

exhibited standard leverage effects, meaning that negative shocks had more impact on price

volatility than positive shocks of the same magnitude. Indeed, an unexpected price decrease

measured by a unit decrease in the standardized residuals 11 / tt decreases the price

volatility of beans by 1.38 %, while an unexpected price increase of the same magnitude

increases its price volatility by only 0.37%. However, for sweet potatoes and millet flour,

increases in volatility appear to be larger when previous returns were positive than when they

were negative of the same magnitude. Hence, past positive shocks (unanticipated price

increases) rise price volatility of sweet potatoes and millet flour by respectively 1.03 and

0.86% and negative past shocks (price decreases) reduce price volatility of sweet potatoes by

0.40% and increase that of millet flour by 0.34%. This type of leverage effect has been named

inverse leverage effects or “inventory effects” by Carpantier (2010) since they do not

display the expected sign. The economic interpretation of such effects can be found in the

theory of storage (Deaton and Laroque, 1992, 1996). Increases in commodity prices may act

as a signal of the depletion of the commodity inventories and therefore positive price shocks

may induce more volatility while negative price shocks may indicate an excess of supply over

demand, reducing thereby current volatility.

1.4.3 Volatility spillover effects

Appendix A.3 reports the estimated results of the multivariate VAR model from equation

(1.9). The optimal lag length of 2 in the VAR model was chosen using the Schwartz criterion.

Results show that current price volatilities are positively and significantly impacted by past

own-price shocks. Hence, higher volatility in the previous months leads to more volatility in

the current one, suggesting persistence in price volatility (Balcombe, 2011). With regards to

volatility spillovers across Ugandan markets, the estimated results indicate that there is no

Essay I

30

clear picture about the presence of spillover effects. We note for example that cassava

volatility is affected positively by shocks to sweet potatoes’ volatility but negatively by

matooke volatility. Maize volatility declines following shocks to cassava and millet flour

volatilities but increases in reaction to shocks to beans volatility. Furthermore, these volatility

spillover effects are globally unidirectional, except for cassava and sweet potatoes. The

matrix of pairwise correlations across different food price volatilities (Appendix A.4) also

gives a similar picture. Although half of the pairwise correlations are statistically significant,

their magnitude is relatively small, below 35%.

Finally, the results from the VAR system can also be used to understand the dynamic

behavior of price volatility through the computation of impulse response functions (IRFs). An

IRF gives the impact of one standard deviation (SD) shock of own- and cross-price volatility

to food price volatility after a certain period of time (here after x months). However, because

the disturbances obtained from VARs may be correlated, I first orthogonalized the

innovations through a Cholesky decomposition in order to get a causal interpretation of the

estimated impulse response functions (Hossain and Latif, 2007). Table 1.7 reports the

responses after one month of food price volatility to Cholesky one SD shock to own- and

cross-volatility as well as the number of months before the effects of the shocks disappear.

Table 1.7 Responses after one month of price volatility to Cholesky one SD shocks

Commodities

Response variable

Matooke Cassava Maize Sweet

potatoes

Beans Millet

Flour

Matooke 0.040

[6]

0.002

[3]

0.001

[1]

0.002

[4]

-0.011

[3]

0.001

[3]

Cassava -0.001

[3]

0.034

[5]

-0.014

[3]

0.022

[3]

-0.025

[4]

-0.005

[1]

Maize -0.001

[2]

0.003

[4]

0.023

[5]

0.007

[2]

0.004

[2]

-0.002

[1]

Sweet

potatoes

0.006

[3]

0.008

[5]

0.003

[2]

0.036

[4]

0.006

[2]

0.001

[4]

Beans -0.001

[3]

-0.003

[3]

0.007

[3]

0.003

[2]

0.033

[4]

-0.001

[1]

Millet flour 0.005

[3]

-0.003

[1]

-0.007

[3]

0.002

[4]

-0.001

[1]

0.019

[5]

Note: The number of months before the effects of the shocks disappear are reported into brackets.


31

A closer look at the table suggests an asymmetric pattern in the distribution of volatility

shocks. First, for all commodities, the effects of shocks to own-price volatility are both

positive and relatively large, implying that food price volatility in Uganda was “self-feeding”.

For example, a one standard deviation shock to matooke and cassava volatilities has led to 4

and 3.4% increases of their own-price volatility after one month relative to their equilibrium

levels. Second, there is no clear evidence of strong market integration across Uganda. Indeed,

the estimated results show that shocks to price volatility of different markets within the

country only have a very marginal and insignificant impact on price volatility in the other

markets, these effects being in all markets less than 1%. Third, in terms of the persistence of

these effects, the table indicates that they last longer when shocks originated from own

markets. For all markets, the effects of one SD shock from own-price volatility take on

average at least four months to disappear against around one quarter in case of shocks to

cross-price volatilities.

1.4.4 Effects of macroeconomic factors on changes in food price volatility

Table 1.8 reports the estimates and robust standard errors of the determinants of price

volatility for 6 commodities using the Seemingly Unrelated Regression (SUR) method. Since

we have 6 commodities and 96 months in the first sub-period (2000m1-2007m12) and 60 in

the second (2008m1-2012m12), a total of 576 and 360 observations, respectively, are

available in the SUR system. The sample is divided into two sub-periods to check for

differential impacts of the potential determinants in periods of low and high volatility.

With regards to the first sub-period (2000m1-2007m12), table 1.8a shows that the coefficient

of MCPI is positive and significant for all commodities which suggests that changes in

consumer price index in Uganda have affected the volatility of food commodity prices. A 1%

increase in the monthly consumer price index is associated with an increase in price volatility

ranging from 0.17% in the case of millet flour to 1.84% for maize, with an average inflation

effect of 0.94%. In periods of high volatility (table 1.8b), the impact of inflation is also

significant and positive for all commodities. On average, the magnitude of the changes in

price volatility during this sub-period is of 1%, higher than that of the relatively stable period.

These results are consistent with other empirical findings that have suggested that not only is

the commodity price volatility generally increasing with changes in consumer price index but

also the impact will be greater in periods of higher price instability (Cashin and McDermott,

Essay I

32

2001; Engle and Rangel, 2008; Roache, 2010; Karali and Power, 2013). For example, Karali

and Power (2013) found that a 1% increase in inflation led to 0.76% in the low-frequency

volatility of heating oil in the US.

Real effective exchange rate volatility MERV is not statistically significant for all commodities

in the first sub-period while in the second its effect is only significant for maize and sweet

potatoes. This insignificance for the majority of the commodities may result from at least two

factors. First, Uganda is relatively self-sufficient in terms of staple foods it consumes, which

limits the influence of changes in exchange rate insofar as financial transactions within the

country are primarily realized in the local currency. Although some commodities are imported

(such as rice, cassava, or beans), the significance of these imports is quiet marginal (Benson et

al., 2008). Second, the Ugandan economy is rather imperfectly integrated to international food

commodity markets (Conforti, 2004; Atingi-Ego et al., 2008; Boysen, 2008; Benson et al.,

2008). And since most contracts in international commodity trade are settled in USD, the role

played by exchange rate volatility in shaping domestic food price volatility is therefore

limited.

As expected, fuel price volatility MFPV has a positive impact on monthly volatilities of most

commodities. However, between 2000m1 and 2007m12, the effect is only significant for two

commodities – matooke and cassava – while between 2008m1 and 2012m12, the effect is

positive and significant for all commodities. In both sub-periods, the impact of 1% increase

was the highest for matooke (0.36 and 1.25%, respectively). All the commodities for which

fuel price volatility has a significant effect are characterized by a lower value-to-weight ratio

and given the long distances across different population centers and the poor transport

infrastructure, fuel price variability is likely to transmit to market prices of these commodities

(Dillon and Barrett, 2014).

Real interest rate volatility MIRV is a poor predictor of food price volatility in Uganda during

both periods and for almost all commodities, its coefficient is insignificant. Unlike the well-

functioning futures markets in developed or some emerging countries, this result is not

surprising for Uganda where the majority of both internal and regional agricultural

transactions are realized out of the banking system and where despite the emergence of

microfinance institutions in the country, credit markets are still in their infancy.


33

Table 1.8 Determinants of changes in food price volatility in Uganda – SUR model

Matooke Cassava Maize

Sweet

potato

Beans Millet

flour

a. Sample period: January 2000 – December 2007

Intercept 0.013

(0.013)

0.003

(0.007)

-0.055

(0.016)***

0.017

(0.012)

0.048

(0.017)***

0.006

(0.007)

MCPI 0.681

(0.207)***

1.194

(0.227)***

1.841

(0.294)***

1.326

(0.357)***

0.984

(0.279)***

0.178

(0.101)*

MERV 0.546

(1.076)

0.994

(0.788)

-0.353

(1.383)

0.629

(1.598)

-1.727

(1.549)

0.605

(0.584)

MFPV 0.356

(0.130)***

0.075

(0.004)***

0.042

(0.317)

0.209

(0.222)

0.066

(0.631)

0.022

(0.106)

MIRV 0.055

(0.043)

0.018

(0.026)

0.049

(0.056)

0.022

(0.057)

-0.062

(0.052)

-0.014

(0.017)

MRFV 0.008

(0.015)

-0.024

(0.009)***

-0.015

(0.028)

0.010

(0.012)

0.029

(0.017)*

-0.002

(0.005)

Harvest1 -0.015

(0.009)*

-0.011

(0.008)*

0.023

(0.013)*

-0.011

(0.018)

0.009

(0.015)

0.003

(0.005)

Harvest2 0.015

(0.013)

-0.009

(0.009)

0.024

(0.012)**

-0.006

(0.017)

-0.008

(0.018)

-0.001

(0.000)***

Planting2 -0.022

(0.011)*

-0.008

(0.009)

0.002

(0.016)

-0.029

(0.017)*

0.054

(0.022)**

-0.003

(0.005)

b. Sample period: January 2008 – December 2012

Intercept 0.055

(0.023)**

-0.011

(0.019)

-0.050

(0.028)*

-0.021

(0.027)

-0.019

(0.021)

0.022

(0.013)*

MCPI 0.908

(0.235)***

0.716

(0.153)***

2.606

(0.279)***

1.028

(0.304)***

0.483

(0.282)*

0.326

(0.121)***

MERV -1.415

(1.252)

0.339

(0.739)

1.168

(0.541)***

1.439

(0.294)***

0.213

(1.134)

1.471

(1.001)

MFPV 1.249

(0.362)**

0.717

(0.309)***

0.414

(0.244)**

0.241

(0.104)**

0.223

(0.124)**

0.241

(0.115)**

MIRV 0.071

(0.106)

0.109

(0.051)**

0.069

(0.108)

0.194

(0.097)**

0.080

(0.096)

0.062

(0.060)

MRFV 0.049

(0.019)**

0.016

(0.001)***

0.022

(0.010)**

0.033

(0.012)***

-0.015

(0.002)***

0.027

(0.008)***

Harvest1 0.023

(0.019)

-0.052

(0.016)***

0.032

(0.011)**

0.043

(0.012)***

0.008

(0.021)

-0.014

(0.014)

Harvest2 -0.013

(0.020)

-0.001

(0.018)

0.071

(0.019)***

0.001

(0.000)*

-0.009

(0.018)

-0.016

(0.012)

Planting2 0.021

(0.009)***

0.004

(0.002)**

0.024

(0.003)**

0.023

(0.005)**

0.043

(0.020)**

0.011

(0.002)**

Note: Robust standard errors into brackets. ***

, **

, and * denoting significance at 1, 5, and 10%, respectively

Essay I

34

Rainfall variability MRFV is found to be an important determinant of food price volatility,

particularly during the second sub-period. This result is recurrent in most studies of price

volatility of agricultural commodities in developing countries insofar as the majority of the

plots cultivated by farmers are essentially rain-fed (Gilbert and Morgan, 2010; von Braun and

Tadesse, 2012; Mirzabaev and Tsegai, 2012). Hence, weather shocks will affect market

expectations about end-of-season yield and price levels, fuelling in turn food price volatility.

The hypothesis of seasonality in food price volatility can be verified through the coefficients

of Harvest1, Harvest2, and Planting2. In sub-period 1, it appears that volatility was higher for

sweet potatoes in the second harvest period compared to the baseline season, whereas it was

lower for millet flour in the first harvest period. During the second sub-period, higher price

volatilities were associated with the second planting season for all the selected commodities

while during the harvest seasons no clear picture emerges from the results. For some

commodities (i.e. maize), more volatility occurs during the second harvest period compared to

the first planting and harvest seasons, while for the others (i.e. sweet potatoes), the first

harvest season appears more volatility than the second one or the first planting season.

Similarly to results from GARCH models, price volatility did not seem to follow a seasonal

path for the majority of the commodities. Consequently, the seasonality hypothesis of price

volatility can only be partially accepted in Uganda, at least for the 6 commodities analyzed in

this first essay. Several empirical studies, essentially in agricultural futures markets, have also

produced mixed results with regards to the seasonal effect on price volatility (Milonas, 1986;

Galloway and Kolb, 1996; Koekebakker and Lien, 2003; Karali and Power, 2013).

We finally check whether the effects of macroeconomic variables vary across different

commodities by running restriction tests. The results from the F –tests reported in table 1.9

indicate that, at the 10% significance level, we reject in both sub-periods the hypothesis that

each macroeconomic variable has an identical impact on price volatility of the six

commodities analyzed. This suggests that, although most macroeconomic variables included

in the SUR model present the expected sign, the magnitude of their effects on food price

volatility in Uganda has been commodity-specific.


35

Table 1.9 F – tests on restrictions across food commodities

Macroeconomic

variables

F - stats p - value

MCPI 58.46 (92.97) .0000 (.0000)

MERV 11.74 (74.65) .0051 (.0000)

MFPV 30.43 (42.86) .0012 (.0001)

MIRV 2.547 (4.95) .0941 (.0018)

MRFV 4.741 (15.33) .0052 (.0001)

Note: The first values concern the sub-period 2000m1-2007m12 while those into parentheses are

related to the second sub-period.

1.5 Conclusions

The purpose of the present study was to investigate the time series behavior of food

commodity prices in Uganda using monthly price data for six staple foods, namely matooke,

cassava, maize, sweet potatoes, beans, and millet flour. Results from unconditional price

volatility analysis revealed that all commodities but beans experienced significant rise in their

price volatility. Hence, when we compare two sub-periods (2000-2007 and 2008-2012) in

terms of changes in price instability, cassava had the highest increase in mean price volatility

(92.9%), followed by millet flour (60%), and sweet potatoes (58.8%). The GARCH (1, 1)

estimation results also indicated that the mean conditional volatility has increased for half of

the commodities analyzed, namely cassava, sweet potatoes, and millet flour. The Exponential

GARCH (EGARCH) model, used to capture possible asymmetric and leverage effects in

price volatilities, found evidence of standard leverage effects only with respect to beans. This

suggests that negative shocks would amplify price volatility of that commodity more

significantly than positive shocks of the same magnitude. Conversely, inventory or inverse

leverage effects were found in the case of sweet potatoes and millet flour since positive

shocks to their price volatilities had more impact than negative shocks.

Results also showed the presence of strong persistence in price volatilities of all commodities

but a relatively complex spectrum regarding the nature of spillover effects across food

markets. Spillover effects were found to be not only moderate compared to inertia effects but

also essentially unidirectional. For instance, shocks to cassava, beans, and millet flour prices

Essay I

36

spilled unidirectionally over maize prices whereas price shocks to matooke and sweet potatoes

affected cassava prices.

These results clearly have important policy implications, particularly in terms of price

stabilization mechanisms. For instance, they suggest that policymakers should be aware that

policies targeting a specific commodity market in the country might also have important

repercussions on other markets, thereby either exacerbating or mitigating the levels of their

prices and volatilities. Although net sellers might benefit from these high prices through

increases of their income, the majority of Ugandan households are either net buyers or purely

consumers of marketed foods and consequently will be negatively affected if the

implementation of price control mechanisms end up accentuating volatilities. It is therefore

crucial to develop and implement measures likely to increase productivity, sustainability and

resilience, particularly in the agricultural sector (i.e. improving access of farmers to credits,

increasing formal job market opportunities, or promoting risk management practices), and to

initiate new transfer programs or improve existing ones so that parts of the gains realized by

net sellers from high prices could be distributed to more vulnerable households.

Finally, the study estimated the impacts of macroeconomic factors on observed price

volatility in Uganda: monthly volatilities of rainfall, overall inflation, real effective exchange

rate, real interest rate, fuel price as well as seasonality effects have been used as potential

drivers. Estimating a Seemingly Unrelated Regression (SUR) model for periods of low and

high price volatilities, I found that, globally, variables that explained the largest part of

observed price volatility included Uganda inflation, rainfall, and fuel price volatilities. The

effects of these factors were more pronounced during the second sub-period. The significant

and globally positive impact of these variables implies that, beyond actions targeting

specifically the agricultural sector such as increased investments in agricultural research and

development and downstream services (storage or processing facilities), additional measures

would be required to stabilize prices and, ideally, reduce their volatility. Thus, actions such as

investments in education, roads, electrification and irrigation projects may play a role in price

stabilization in Uganda.

37

Essay II

Welfare effects of food price changes in Uganda under non-

separability

How relevant is the net market position?15

2.1 Introduction

To what extent do large food price changes affect household welfare? Who gains and who loses

from these price changes? How are these welfare effects distributed across different households?

And specifically, what happens when market failures are accounted for? These questions and many

others have been at the core of recent debates among development economists, government

authorities, NGOs, and the media who fear about the risk of poverty traps, increased vulnerability

and food insecurity of the least endowed households on the one hand, and on the other the risk of

political turmoil, economic fragility, and social tensions that high food prices might induce

(Bellemare, 2015). This concern is particularly germane in developing countries where food

consumption accounts for the largest share of households’ total expenditures and where the poor

often spend disproportionally a large part of their income on food (Mghenyi et al., 2011; Dybczak,

et al., 2010; Akson and Hoekman, 2010).

Although Uganda is relatively insulated from international markets due to its landlocked position,

the Ugandan price index of food commodities has been steeply rising since March 2008, in sharp

contrast with the period before. Indeed, food prices have been relatively stable between 2000 and

early 2008, rising annually at 5% (UBoS, 2010). From that period onwards, they have continued to

rise due to internal dynamics (rainfall variability, fuel price inflation, exchange rate volatility,…),

international food price crisis, and increased demand from neighbor countries (Kenya, DR Congo,

and Burundi, among others). Even though high food inflation ceased off between September 2009

and July 2010, prices remained at higher levels and Uganda experienced again high food prices

since September 2010, with prices of some commodities like sugar, fish, and milk rising by over

200 percent.

15

This second essay was written in co-authorship with Gabriella Berloffa.

Essay II

38

Several studies have examined the impact of rising food prices in Uganda (Dorosh et al., 2003;

Conforti, 2004; Bussolo et al., 2007; Benson et al., 2008; Boysen, 2009; Ulimwengu and Ramadan,

2009; Kaspersen and Føyn, 2010; Silmer, 2010), focusing either on the extent of price transmission

between international and domestic prices or on the impacts of soaring global prices on poverty.

However, all these studies suffer from two main drawbacks. First, farmers’ behavior is modeled

assuming that production and consumption decisions are two separable problems, leading to a

recursive model (Singh et al., 1986). Notwithstanding its attractiveness, there has been little

empirical evidence supporting the recursivity hypothesis, due particularly to imperfections

characterizing rural markets in developing countries16

(Lopez, 1984; Benjamin, 1992; Jacoby,

1993; Skoufias, 1994; Arcand and d’Hombres, 2006). In this study, we explicitly test the

separability hypothesis under labor market imperfections. This allows us to identify the role played

by virtual or shadow wages in estimating the welfare effects of price changes (Sonoda and

Maruyama, 1999). Second, in previous studies, the estimation of direct and substitution welfare

effects is done through different simulations applied to data collected before the actual food price

shocks occur, and therefore they only identify households potentially vulnerable to rising food

prices rather than those with actual welfare losses (Headey and Fan, 2008). Instead, we use three

waves among the latest Uganda National Panel Surveys (UNPS) spanning over the years 2005-

2011 to estimate the actual welfare effects of increased food prices.

To analyze the welfare changes of Ugandan households consecutive to food price instabilities, this

study applied a sequential procedure consisting in three steps. First, virtual and shadow wages of

self-employed agricultural households are derived by estimating a stochastic production frontier

function following the Battese and Coelli’s (1995) Maximum Likelihood-random effects time-

varying inefficiency effects model and the Sherlund et al.’s (2002) and Barrett al.’s (2008)

approaches. After testing for the separability hypothesis, we then estimate expenditure and price

demand elasticities from a food demand system using the Quadratic Almost Ideal Demand System

(QUAIDS) model proposed by Banks et al. (1997) and estimated through a Non-linear Seemingly

Unrelated Regression (NSUR) model in presence of censoring and endogeneity. To take account of

year-specific effects, the heterogeneity of Ugandan households in terms of their food net market

position and the impact of labor market frictions, these demand elasticities were estimated for each

year and sub-group of households (non-agricultural households, significant net sellers and net

16

These imperfections include: farmers’ preferences towards working on- or off-farm (Huffman, 1980; Lopez, 1986); imperfect substitutability between market-purchased and home-produced food (Imai et al., 2011); missing labor and/or food markets (Singh et al, 1986; de Janvry, Fafchamps, and Sadoulet, 1991, Taylor and Alderman, 2003); presence of fixed and/or variable transaction costs that create a wedge between consumer and producer prices (Key et al., 2000; Henning and Henningsen, 2007)


39

buyers, and insignificant net sellers and net buyers) for both separable and non-separable models.

The final step consists in computing money-metric welfare measures of food price changes with

and without the possibility of substitution across commodities.

The remainder of this second essay is organized as follows. In section 2, an agricultural household

model is presented and its theoretical predictions are analyzed. Particularly, our conceptual

framework seeks to identify potential deviations from the standard household model when labor

market imperfections are accounted for and household’s net positions in both food and labor

markets are incorporated into the analysis. In section 3, we present and discuss the estimation

strategy adopted for the computation of welfare effects of price changes. Data descriptions and the

construction of some key variables for our econometric estimations (consumer food prices,

commodity grouping, and net food market position) are presented in section 4. Section 5 presents

and discusses the empirical findings before the conclusion in section 6.

2.2 Theoretical model

In this section, we present a simple theoretical model of the price effects on farmers’ welfare with

perfect and imperfect labor markets given that labor is, by far, the most important variable input in

the production process of Ugandan farmers and the internal labor market, particularly in rural areas,

is very thin and generally relies on the family force17

. Consider a farmer that produces a cash crop

cQ devoted solely to the market and sold at price cp and a staple food aQ consumed and/or sold at

market price ap , using family labor o

fL , hired labor hL , other variable inputs V and quasi-fixed

inputs (land and/or capital) A. He maximizes his utility by consuming three types of goods: a non-

food good (cn) purchased at market price np ; food consumption (cf), either market-purchased ( m

fc )

at price ap or produced on the farm ( afc ), and leisure

Lc . By simplicity, afc and m

fc are assumed to

be perfect substitutes so that af

mf

af

mff ccccc ),( . The farmer receives his income from farming

activities, off-farm employment f

fL , and non-labor incomes (E). His problem can be formalized as

follows:

LnfuC

cccCzCUUMax ,,,;

subject to

17

These imperfections can result from heterogeneity betwen family and hired labor (Benjamin 1992; Deolalikar and Vijverberg 1983, 1987; Thapa, 2003), the presence of transaction costs (Key et al., 2000), or limited access to employment opportunities (Archand and d’Hombres, 2006; Le, 2012)

(2.1)

(2)

(3)

(4)

Essay II

40

VLLXQQQzAXQG h

o

fcaq ,,;,,0;,,

0 L

o

f

f

f cLLT

ELfQpQpLgVpcpcp f

fccaahvnnfa

In equation (2.1), (.)U is an instantaneous farmer’s utility function, assumed monotonically

increasing and strictly quasi-concave; uz is a vector of exogenous shifters in utility. Equation (2.2)

gives the technology constraint and relates the farm productions ca QQ , to inputs AVLL h

o

f ,,,

through a multi-output, multi-input transformation function (.)G , assumed concave and continuous

in inputs (Lau, 1976), with qz , a vector of production shifters. The farmer is also constrained by the

time endowment (equation 2.3), where the total time available (T) is allocated to on-farm labor, off-

farm labor and leisure. The farmer finally faces a budget constraint (equation 2.4) specified in a

way that accounts for labor market imperfections. Following Henning and Henningsen (2007) and

Glauben et al. (2012), off-farm revenues and hired labor costs are specified as functions )( f

fLf and

)( hLg , respectively. In case of a perfect labor market, both )( f

fLf and )( hLg are linear functions

f

f

f

f wLLf )( and hh wLLg )( , respectively. Thus, the marginal revenue of off-farm employment

and the marginal cost of hired labor are constant and given by the exogenous market wage rate w.

Imperfections in the labor market can be captured by modeling )( f

fLf and )( hLg as non-linear

functions. In particular, off-farm revenues are an increasing and strictly concave function of f

fL :

0;02

2

)(

)()(

ff

ff

ff

ff

L

Lf

L

Lf,

while the costs of hired labor are an increasing and convex function of Lh:

0;0

2

2

h

h

h

h

L

Lg

L

Lg

The farmer will choose the levels of consumption goods, on- and off-farm family labor, hired labor,

and variable inputs to maximize his utility in (2.1), under the resources and time constraints (2.2) to

(2.4).

Let , and be the Lagrange multipliers associated with the budget, technology and time

constraints, respectively. The FOCs for this problem are:

(2.2)

(2.3)

(2.4)

(2.5)

(2.6)


41

ELfQpQpVpLgcpcp

cLLT

zAXQG

p

QQQip

ccCip

ffccaavhnnfa

Lff

of

q

L

f

L

G

L

g

L

G

vV

G

caiQ

G

c

U

nfic

U

ff

of

nh

i

L

i

0

0;,,

0

0

0

0

,0

0

,0

.

.

..

.

.

.

.

From the FOCs, we have that:

f

f

o

fL L

f

L

G

c

U

...

The shadow wage (i.e. the opportunity cost of time) is therefore given by ff

L

fw

.*

. In case of a

perfect labor market, the shadow wage is equal to the exogenous market wage w , leading to a

separable model, in which the farmer’s labor allocation decisions are not affected by consumption

preferences, and no tradeoff exists between farm work and leisure (Taylor and Alderman, 2002). If

instead, the labor market is imperfect, then ww

* . The shadow wage *w now depends on

farmer’s preferences through the marginal utilities of wealth ( ) and time ( ). The value of these

multipliers will depend on the vector of all exogenous market prices of consumption and production

goods vnca pppp ,,,p , non-labor incomes, time endowment, consumption and production

shifters:

qu zzTEww ,;,,**p

The solution to the farmer’s maximization problem leads to a system of output supply

),;,( *

quii zzwQQ p and input demands ),;,( *quii zzwXX p , off-farm labor supply )( *wLL

ff

ff ,

and a consumption system ),;,,( *quii zzYwCC p , where EcTwY L ** , and

ofhvccaa LLwVpQpQp ** .

(2.7)

(2.8)

Essay II

42

Hence, a change in market prices will lead to a change in the consumption vectors, output supply,

input demands, as well as in the shadow wage. Following the standard non-separable household

model (NSM) literature (Singh et al., 1986; Strauss, 1986; de Janvry et al., 1991), this change can

be decomposed into two components. Concretely, for a farmer producing a quantity aQ and

consuming fc of the staple food, the impact of a change in ap on consumption is given by:

a

f

wa

f

wa

f

a

f

p

w

w

c

p

c

p

c

p

c

*

*

*

*

*, **

which, expressed in terms of elasticities, becomes:

effectvirtual

af

hfHf

effectdirect

ffaa

aHfaf

pwEYcEY

LLwwcE

YcEY

cQppcEpcE

**

*/

///

where jiE / represents the elasticity of i with respect to j, and Hfc the Hicksian demand of the

staple food. The first term in the right-hand side of equation (2.10) represents the direct effect of

changes in the exogenous market price on the farmer’s consumption, keeping constant the shadow

wage. This coincides with the effects of price changes that we would have derived in a separable

household model (SM). Indeed, in a separable model, since the virtual effect in (2.10) is equal to

zero, an increase of the food price ap induces a clear negative consumption effect if the household is

a net buyer ( 0 fa cQ ) given that both the income and substitution effects are negative. For net

sellers, the sign is a priori ambiguous: the effect will be positive if and only if the total income

effect outweighs the negative substitution effect.

In the case of non-separability however, we need to consider also the virtual effect, which captures

the adjustments of consumption to the changes in the shadow wage ( *wcE f ) and due to changes

in market prices ( apwE * ) (Strauss, 1986; Sonoda and Maruyama, 1999). Since theoretically the

Hicksian elasticity 0* wcE Hf , the virtual effect will have the sign of the elasticity apwE * if

farmers are net sellers of labor (i.e. if family off-farm labor is larger than hired labor, which means

that changes in virtual family earnings exceed changes in virtual farm labor costs). In particular, if

the increase in ap increases the shadow wage, and farmers are net buyers of food and net sellers of

labor, the elasticity of food consumption to its price will be less negative under non-separability, or

(2.9)

(2.10)


43

even change its sign from negative to positive. In other words, under non-separability, food

consumption will decrease less or even increase as the price of food increases. If instead, the

increase in ap reduces the shadow wage, farmers who are net buyers of food and net sellers of

labor, will have a larger elasticity (in absolute terms) under non-separability (i.e. food consumption

will fall more after an increase in its price).

The reasoning is similar for the other cases, which are summarized in the following table.

Table 2.1 Theoretical effects of an increase in food prices on food consumption, by net positions in food and labor

markets

Labor net sellers: 0 hfLL Labor net buyers: 0 hf

LL

0* apwE 0* apwE 0* apwE 0* apwE

Food net buyers:

0 fa cQ

(-) direct effect

(+) virtual effect

Total effect in

NSM: less negative or positive

(-) direct effect

(-) virtual effect

Total effect in

NSM: more negative

(-) direct effect

(-)/(+) virtual effect

Total effect in

NSM: Indeterminate

(-) direct effect


Total effect in

NSM: Indeterminate

Food net sellers:

0 fa cQ

(-)/(+) direct effect

(+) virtual effect

Total effect in

NSM: less negative

or more positive


Negative virtual effect

Total effect in NSM:

more negative or less

positive




Indeterminate




Indeterminate

Note: (-) and (+) denote negative and positive effects, respectively. NSM: Non-separable household model

Uncovering the sign of the shadow wage elasticity

It is therefore important to derive the expression and sign of shadow wage elasticity apwE * upon

which largely hinge the sign and magnitude of af pcE / . By using the expression of the time

constraint (equation 2.3) at the optimum ( 0),;,,(),;,( *** quLffqu

of zzYwcwLzzwLT pp ), and

applying the implicit function theorem to it (de Janvry et al., 1991; Henning and Henningsen,

2007), we get:

aaa

p

L

p

f

p

o

f

wa

L

wa

o

f

a

w

c

w

L

w

L

p

c

p

L

dp

dw

***

**

*

(2.11)

Essay II

44

The numerator in (2.11) represents the direct disequilibrium on the ‘household’ labor market

created by a change in ap , whereas the denominator captures the indirect disequilibrium created by

the change in the shadow wage caused by a change in ap . In order to get the intuition of how this

works, consider the case in which there is no possibility to work off-farm. When ap increases, the

consumption of food decreases and the marginal value of income increases. Therefore a household

would like to increase its income, by increasing farm production. This increases on-farm labor

demand

0

*wa

of

p

L, but household labor supply may not increase sufficiently

***

and0

wa

L

wa

of

wa

L

p

c

p

L

p

c. In order to restore the equilibrium on the labor market we

would need an increase in the shadow wage if the labor supply is upward sloping

0

*ap

L

w

c ,

or if it is downward sloping

0

*ap

L

w

c, but steeper than the labor demand

aa p

of

p

L

w

L

w

c

**.

If instead, the labor supply is downward sloping, but flatter than the labor demand, in order to

restore the equilibrium we would need a reduction in the shadow wage.

On the contrary, if the direct effect of the increase in ap is an excess of labor supply, the

equilibrium will be restored by a decrease in the shadow wage if the labor supply curve is upward

sloping or if it is downward sloping but steeper than the labor demand, and by an increase in the

shadow wage if the labor supply is downward sloping, but flatter than the labor demand.

In general, however, under non-separability, it is quite difficult to predict the effect of an increase in

ap on both the shadow wage and food consumption. If the direct effect in equation (2.10) dictates

the total effects, then increases in food prices will lead to a reduction of food consumption for net

buyers but the effect will remain ambiguous for net sellers. If instead, the degree of labor market

imperfections is relatively high such that the indirect component of equation (2.10) is predominant,

then the price effect on consumption is theoretically unclear and can potentially lead to abnormal

behaviors (de Janvry et al., 1991). As a direct consequence of this ambiguity, we are theoretically

unable to determine both the sign and magnitude of the welfare effects of price changes. However,

we can derive a money-metric measure for the welfare effect (the compensating variation, hctCV ),

as a function of the elasticity of the shadow wage to food prices.


45

Let ),( upe be the expenditure function associated with the household utility maximization problem,

i.e. Lnannfa hppwhphpupe ,...),(),( * where hi is the Hicksian demand for good i. The CV is

generally defined as: ),(),( 0111 upeupeCV , i.e. it measures the net revenues of the planner who

must compensate the households. Since in our case income is not exogenous, we have:

))()((),(),( 0*1*0011 pYpYupeupe , i.e.:

*01000111 ),(),(),(),( YupeupeupeupeCV

If we take a first-order Taylor series expansion of ),( 01 upe and )( 1* pY , both around p0, we get:

nhfnnn

ahffaaa

p

wLLCpp

p

wLLCQppCV

*01

*01 )()(

where in (2.13) we used the identities:

)(,),( 0*000 pYpCuph fa , and ff

ofLL LLTpYpCuph ))(,(),( 0*000

Expressed in terms of elasticities, (2.13) becomes:

ihfiiii

i

nai

pwELLwCQpp

pCV |**

,

where yxE | denotes the total elasticity of x with respect to y.

Note that, when there is no shadow wage effect, (2.14) reduces to the CV capturing only the

immediate effect of price changes, as described for example in Vu and Glewwe (2011). The

expressions for the short run effect can be derived by taking second order Taylor series expansion

of the expenditure function (Friedman and Levinsohn, 2002; Porto, 2010; Vu and Glewwe, 2011).

Ignoring the terms involving the product of two elasticities and two changes in prices (or the second

order effect of the change in prices on the shadow wage), we have:

effectsonsubstituti

iiiHij

Hi

j

j

i

i

najnai

effectsorderfirst

ihfiiii

i

nai

CppwEwCEpCEp

p

p

p

pwELLwCQpp

pCV

|||2

1

|

**

,,

**

,

where *| wCE Hi represents the Hicksian compensated elasticity of x with respect to y.

(2.12)

(2.13)

(2.14)

(2.15)

Essay II

46

Whether in non-separable models the compensating variation CV is larger or smaller than in

separable models, it depends on both the household positions in the food and labor markets (net

buyers or net sellers), and the sign of the elasticity of the shadow wage with respect to food prices.

2.3 Estimation strategy

In this section we present our empirical strategy to estimate econometrically both the separable and

non-separable models to assess if and to what extent labor market imperfections influence the sign

and magnitude of household welfare effects of price changes. Given the above theoretical

framework, the unobservability and endogeneity of the shadow wage *w , the estimation strategy

proceeds in three steps. First, we estimate the shadow price of labor and test for the recursivity

hypothesis. Second, given the shadow wage thus obtained, we estimate a Quadratic Almost Ideal

Demand System (QUAIDS), and finally compute money-metric welfare measures of price changes

under both separability and non-separability.

2.3.1 Estimation of the shadow wage and test of the recursivity hypothesis

One of the common features of the agricultural sector in most developing countries is the

predominance of small-scaled farmers that often rely on their family members during planting and

harvest seasons. These members are generally unpaid although they benefit from the production

outcomes through consumption or distribution of part of the farm profits. Under the hypothesis of

perfect labor markets and perfect substitutability between family and hired labor (Deolalikar and

Vijverberg, 1987), one can impute the wages for on-farm family labor using the observed market

wages for labor of similar requirements. However, farmers may attach subjective values to their on-

farm labor that deviate from the market wages or the labor market may simply be missing or

incomplete due to different sources of market frictions18

(de Janvry and Sadoulet, 1991). In this

case, the separability hypothesis will break down and one will need to estimate these subjective or

shadow prices of on-farm labor. To derive the shadow wages, we build upon Jacoby’s (1993)

structural labor supply estimation approach, extended by Sherlund et al. (2002) and Barrett et al.

(2008) who relax the assumption of allocative efficiency made by Jacoby– equality between the

marginal revenue product of labor and market wage.

18

In many rural areas of developing countries, farmers are generally insulated from local markets due to high transportation costs, are often constrained by liquidity and have very limited access to both formal and informal credits. In this context, hiring labor might represent a significant part of input expenditures that most farmers cannot afford, thereby deciding to employ exclusively family labor in the production process.


47

The Sherlund et al.’s and Barrett et al.’s approach is a sequential estimation strategy that can be

summarized as follows. In the first step, we estimate a stochastic frontier production function on the

whole sample of agricultural households following the Battese and Coelli’s (1995) approach to

derive the marginal product revenue of labor LMRP , using average real market prices of

commodities produced. Formally, let htY denote the total production (in values)19

by a farmer h in

year t; htX be a vector of productive inputs used by farmer h at time t (such as on-farm family labor

ofL , hired labor hL , land size and other variable inputs (fertilizer, seeds, or pesticides); htZ be the

vector of household characteristics (such as household size, education and sex of the household’s

head, region- and year-specific dummies) and ht be the vector of environmental factors (like labor

quality, types of land slope or irrigation). The stochastic production frontier function in the context

of panel data is written as follows:

hththththt VUXFY ,

where hthtXF , is the production frontier; htU is the technical efficiency parameter of production

assumed to be function of a set of observable characteristics htZ (i.e. ,0' hththt ZU with the

random variable ht distributed 2,0 N and truncated from below at the truncation point 'htZ

(Barrett et al., 2008). htV is the error term assumed independently and identically distributed

2,0 vN . For the empirical analysis, we opt for a flexible translog specification as an approximation

to the unknown true production frontier hthtXF , (Sherlund et al., 2002):

thhthtjhtiht

I

i

I

jij

I

iihtiht VUXXXY

lnln2

1lnln

1 110

where 0 , i , ij and are unknown parameters to be estimated.

The Battese and Coelli’s panel data estimator is a method of maximum likelihood that

simultaneously estimates the parameters of the stochastic production frontier and the technical

inefficiency effects. Both the market prices and the estimated parameters from the stochastic

frontier are used to derive the estimated marginal product revenue of labor LPRM ˆ .

The second step consists in estimating the allocative inefficiency scores for the subsample of

farmers that supply off-farm labor ffL and report a wage w . Using the estimated LPRM ˆ and observed

19

Using values of production instead of physical quantities aims at reflecting the multi-crop nature of most farmers in Uganda and enables the aggregation of different crop productions into a single monetary unit.

(2.16)

(2.17)

Essay II

48

market wages w , the allocative inefficiency AI is defined as LPRMwAI ˆ/ln which is equal to 0 in

case of technical efficiency LPRMw ˆ or equivalently 0htU .

To obtain the estimated shadow wages, we first predict deviations between LPRM ˆ and market wages

w by regressing the allocative inefficiency on a set of household characteristics excluded in the

estimation of the stochastic production frontier equation. These variables include the age (and its

squared value), sex, and the level of education of the head, his marital status, the estimated values

of livestock owned by the household, regional indicators (dummy variables for each region), and

land endowment (land holdings per household member). Second, given the estimated LPRM ˆ from

the first step and the imputed allocative inefficiency scores IA ˆ from the second step, the imputed

shadow wage *w for households that did not supply labor to the market is computed as follows:

LPRMIAw ˆˆexpˆ *

Finally, having estimated the shadow wages, a simple separability test can be carried out by

checking whether the shadow wage distribution for self-employed agricultural households is

significantly identical to the distribution of observed market wages for off- farm workers. The

rejection of the null hypothesis of equal distributions between these two sub-groups of agricultural

households will thus suggest that the recursivity assumption is not supported by the data in hand.

2.3.2 Food demand system

On the consumption side, the preferences of the household (equation 2.1) are estimated through a

Quadratic Almost Ideal Demand System (QUAIDS) model proposed by Banks et al. (1997) which

is a flexible functional form that incorporates nonlinear effects and interactions between prices and

expenditures in the demand relationships. In terms of budget shares, the QUAIDS model has the

following form (Banks et al., 1997):

n

j

i

ijijiia

x

ba

xps

1

2

)(ln

)()(lnln

PPP

where x is the total value of food consumption, xcps iii / are consumption shares for each good i;

jp are consumer prices of commodity j and P is a price index; i , ij , i , i are unknown

parameters ; and :

n

ii

n

i

n

i

n

jjiijii

ipbpppa11 1 1

0 )(,lnln2

1ln)(ln

PP

(2.18)

(2.19)

(2.20)

(22)

(23)


49

Theoretical restrictions of adding-up, homogeneity and symmetry are imposed to the model in terms

of its parameters. Adding-up restriction requires

n

i

i

n

i

ij

n

i

n

i

ii

111 1

0,0,0,1 . Homogeneity

implies

n

i

ij

1

0 and symmetry requires jiij .

However, the presence of zero values in the consumption of certain commodities and the

endogeneity of household total expenditures and shadow wage need to be accounted for to avoid

spurious estimations of equation (2.19).

Zero expenditures on certain food items may come from various sources: shortness of the recall

period, non-preference, non-affordability, purchase infrequency, non-availability, self-consumption

(Boysen, 2012). Since an important proportion of households reported zero consumption in

Ugandan surveys, the dependent variable in equation (2.19) becomes censored and estimating the

QUAIDS model without controlling for the expenditure censoring will lead to biased estimates. To

deal with censored data in the QUAIDS model, we follow the two-step procedure proposed by

Shonkwiler and Yen (1999). In the first step, households decide whether to consume a good i or not

through the estimation of a standard probit model iiii zd , where id is unobserved

counterpart of a binary outcome id that takes 1 if the household did consume the good i and 0

otherwise; z is a vector of household demographics and regional dummies for the model

identification; i is the error term. Conditional on the decision to consume the good i¸ consistent

parameters of the QUAIDS are estimated in the following way (Barslund, 2011; Boysen, 2012):

iiiiiiiii zxfzs )ˆ(),()ˆ(*

where )ˆ( ii z are estimates from the first step; and are the standard normal and cumulative

density functions, respectively. i is the error term.

Expenditure endogeneity appears whenever the household expenditure allocation process across

products is significantly affected by unobserved factors not captured by explanatory variables

included in the estimation of is (Bopape, 2006). To test for expenditure endogeneity, we use

household income and its square as IVs for total household food expenditure and proceed in two

steps. In the first stage, we regress household expenditures on consumer prices, household

demographics, and total income (and its squares). In the second stage, the residuals from step 1 ( )

are then augmented to the each budget share equation. The null hypothesis of expenditure

exogeneity is then tested by checking whether the coefficient of is statistically significant. Given

potential correlation between the error terms of different budget shares, we also run the endogeneity

(2.21)

Essay II

50

test using a restricted SUR model (Bopape, 2006) and determine whether the coefficients of are

jointly significant across all budget share equations. The estimation of the QUAIDS is done by

applying a modified version of the Nonlinear Seemingly Unrelated Regression (NSUR) proposed

by Poi (2008) to include censoring due to zero expenditures and endogeneity of expenditure and

shadow wage.

2.4 Data and descriptive statistics

In this section, we describe the Uganda National Panel Surveys (UNPS), the procedure for

constructing the variables used for our empirical analysis, and present their descriptive statistics.

2.4.1 Samples

We use three waves of the Uganda National Panel Surveys (UNPS) collected by the Uganda Bureau

of Statistics (UBoS) in 2005/2006 (hereafter UNPS-2006), 2009/2010 (UNPS-2010), and

2010/2011 (UNPS-2011), covering periods of both low and high prices. All the surveys were based

on a two-stage stratified random sampling design and therefore allow for comparisons across

surveys and aggregation over time. In the first stage, Enumeration Areas20

(EAs) were selected

from the 4 geographical regions of the country and grouped by districts and rural-urban locations

(UBoS, 2010). In the second stage, around ten households in each EA were selected by simple

random sampling. Each household was then visited twice in order to capture seasonalities in the

agricultural production module21

. Among the 3,123 targeted households in UNPS-2006, the UBoS

was able to track 2,607 households in 2009/10, among which only 2,566 had complete information

(Ssewanyana and Kasirye, 2012), which represents an attrition rate of 17,8%. And among the 2,566

households tracked in the UNPS-2010, 2,390 were re-interviewed in the UNPS-2011 with only

2,310 households having complete information in all the three waves. Because our interest is in

understanding the welfare consequences of large food price changes in Uganda during the 2005-

2011 period, we only keep households with complete information tracked in all the three surveys,

giving us a balanced sample of 2,310 observations over three periods22

. The panel surveys provide

20

An enumeration area represents “the smallest ground area, mapped with definite boundaries within which a study

or interview is carried out” (UBoS, 2012: 32). 21

In the UNPS-2006, households were first visited between May and October 2005 and then between November 2005 and April 2006. In the UNPS-2010, first visits occurred between September 2009 and January 2010 while the second were conducted between February 2010 and August 2010. For the last wave, first visits were conducted between October 2010 and March 2011, while the second were between April and September 2011. 22

Given the relatively high attrition rate (26% from 2005 to 2011), we first checked whether attritors and non-attritors were statistically different in terms of household characteristics and consumption patterns. In Appendix B.1 we report the procedure used to test for attrition bias in the data and compute inverse probability weights (IPW) to correct for it.


51

detailed information on household demographics, production (labor23

and non-labor inputs, outputs

harvested and sold), consumption (food and non-food commodities), land holdings and livestock

ownership, among others. For each commodity, they list the measurement unit as well as the

quantities and values for different types of consumption (household consumption from purchases,

consumption away from home, consumption from home production, and consumption of goods

received in-kind). Different recall periods were used depending on the nature of the expenditure

item: from a seven-day recall period for food consumption to one year for durable, semi-durable

and non-consumption expenditures (taxes and duties, pension, social security contribution,

remittances, gifts, contribution to funerals...).

2.4.2 Consumer prices, commodity grouping, and consumption shares

Information on consumer prices is given in terms of unit values, obtained by dividing values by

quantities. Seen as the highest acceptable price or “subjective price” (Pons, 2011), these unit values

might contain measurement errors and reflect both quality and price differences (Deaton, 1988,

1997) and therefore require a correction before being used as a proxy of prices. To that end, we

followed the approach proposed by Deaton (1988) whose basic idea is that, insofar as households

within the same village (cluster) are usually surveyed within a period of relatively few days, they

should normally face the same prices (Boysen, 2012). We first constructed clusters as a

combination of EAs and districts, and got 321, 337, and 356 clusters for each panel, respectively.

For each commodity in a specific cluster, we generated mean unit values that are then regressed

through OLS over household characteristics (households’ physical assets, household composition,

education, gender, age of the head...), cluster and other regional dummies. The predicted values for

the estimation are then used as imputed consumer prices24,25

.

Furthermore, given the large number of goods consumed by households26

, the estimation of

consumption share equations would become cumbersome without prior adjustments. In practice, the

solution consists in grouping commodities in order to reduce the number of goods to a relatively

23

In the surveys, the agricultural modules measure the time spent working on-farm in person-days which reflect both the size of team and the number of days spent. For each plot, the surveys report the number of household members involved and the total person-days. For hired labor, only the total number of person-days per plot is reported for male, female, and children (except in the 2005/6 survey). Hence, to convert these person-days into hours of on-farm (

ofL ) and hired ( hL ) labor, we assume that for each day-work, adults (children between 6 and 15 years) work on

average 8 (6) hours. 24

Missing prices were approximated using the average prices at the cluster levels, and if still missing, at the district or regional levels. 25

We also applied other alternative methods to check for the robustness of our results. For example, Attanasio et al. (2013) propose to use the median unit value at the cluster level as a measure of consumer price. However, this approach gave relatively similar results as the Deaton’s. 26

The panels collected information on more than 60 different food, beverage and tobacco commodities.

Essay II

52

more manageable figure27

. As an attempt to obtain a reasonable number of parameters and referring

to both commodities which are normally close derivatives of one another28

and previous studies on

demand systems in Uganda (Ulimwengu and Ramadan, 2009; Boysen 2012), we constructed 10

food groups plus leisure29

: matooke )( 1k , cassava )( 2k , potatoes )( 3k , maize )( 4k , beans )( 5k ,

meat & fish )( 6k , fruits & vegetables )( 7k , fats & oils30

)( 8k , alcohol & tobacco )( 9k , and other

foods for the remaining commodities )( 10k . The prices for each food commodity group were

computed as weighted means of commodities in that group, the weights being the mean

consumption shares of each item. To approximate the value of leisure time, we use two types of

information. In the separable model, we use the reported market wage31

obtained by those who

worked for pay during the last 12 months. For those who did not report any wage, we impute their

value using the average market wage at each cluster/district level. In the non-separable model, the

shadow wage is used as the opportunity cost of leisure time. To obtain the total value of household

food consumption and therefore food consumption shares, consumption from home production has

been valued using market prices under the assumption that market-purchased and home-produced

goods are perfect substitutes32,33

.

27

Theoretically, there exist two alternative approaches for commodity grouping. The first approach -called the composite commodity theorem- asserts that we should group commodities whose prices are moving in parallel. However, since relative prices fluctuate considerably, the applicability of this approach is rather limited. The second approach, known as the separability theorem, states that if preferences are weakly separable, then we can construct independent sub-utility functions for each group and sum them up to get total utility. The weak separability hypothesis can be tested using for instance the F and Likelihood ratio version tests. In case of rejecting the null hypothesis of weak separability, the commodity grouping strategy must be guided by both the nature of the problem in hand and previous related studies (Abdulai and Aubert, 2004). 28

Like cassava flour and grain, maize grain and flour, sweet and Irish potatoes, different types of meat (beef, pork, goat, chicken,…) 29

The amount of leisure is obtained using the time constraint (equation 2.3) : of

ffL LLTc . Assuming that

each household member aged below (above) 15 years has 12 (16) hours available per day for work/leisure (Henning

and Henningsen, 2007; Tiberti and Tiberti 2012), the total annual time available for a household with 1n members

below 15 years and 2n above 15 years, 21 *16*12*365 nnT . f

fL and o

fL are the total annual hours for

off- and on-farm family labor, respectively. 30

Cooking oil, margarine, ghee, sugar, salt,… 31

It is the ratio between the total payments (in cash and in-kind) divided by the total number of hours 32

This assumption can be tested by computing the shadow price of consumption from home production (Arslan and Taylor, 2008). One can then regress these shadow prices over market prices and other household characteristics and test whether the coefficients associated with market prices are not significantly different from one. However, given the focus of the present study on labor market imperfections rather than missing or imperfect food markets, this assumption was deemed reasonable. 33

In this study, we prefer the use of “consumption shares” in lieu of “budget shares” and “total value of food consumption” rather than “total food consumption expenditures” given the inclusion of the imputed values of both consumption from home production and leisure time, which are not actual purchases/expenditures.


53

In table 2.2, we report the percent changes in real consumer prices34

of food commodity groups

between 2005/06 and 2009/10, 2009/10 and 2010/11, and between 2005/06 and 2010/11. Between

2005/06 and 2010/11, most commodity groups were characterized by soaring prices, with cassava,

maize, and beans displaying more than 200% increases; potatoes, fruits and vegetables, and other

foods more than 100%; matooke, meat and fish, and alcohol and tobacco more than 50% increases.

Table 2.2 Changes in real consumer prices of commodity groups between 2005/6 and 2010/11

Commodities Changes in real consumer prices between…

…2005/6

and 2009/10

…2009/10

and 2010/11

… 2005/06

and 2010/11

1k 0.472 (0.299) 0.216 (0.297) 0.745 (0.367)

2k 1.716 (0.117) 0.569 (0.185) 2.493 (0.540)

3k 0.915 (0.269) 0.511 (0.493) 1.712 (0.447)

4k 1.555 (0.289) 0.197 (0.231) 2.296 (0.642)

5k 0.827 (0.180) 0.413 (0.103) 1.069 (0.341)

6k 1.63 (0.209) 0.235 (0.169) 2.602 (0.679)

7k 0.829 (0.105) 0.141 (0.067) 0.953 (0.164)

8k 0.146 (0.335) 0.327 (0.354) 0.471 (0.416)

9k 0.514 (0.419) 0.099 (0.090) 0.633 (0.565)

10k 1.23 (0.398) 0.179 (0.210) 1.804 (0.867)

Overall 1.392 (0.152) 0.214 (0.087) 1.467 (0.170)

Note: Item indices ik : 1: Matooke; 2: Cassava; 3: Potatoes; 4: Maize; 5: Beans; 6: Meat and fish; 7: Fruits and

vegetables; 8: Fats and oils; 9: Alcohol and tobacco ; and 10: Other foods. Standard deviations into brackets.

Comparing different sub-periods, real consumer prices skyrocketed between 2005/06 and 2009/10.

Indeed, the overall percent increase was 139.2% against 21.4% between 2009/10 and 2010/11.

During the first two waves, cassava and beans exhibited the highest price increases with 172% and

163%, respectively, while fats and oils and matooke displayed the lowest changes in their real

prices (14.6% and 47.2%). Compared to the changes between 2005/06 and 2009/10, real price

changes, though still positive for all commodity groups, slowed down in 2010/11. Cassava and

potatoes presented the highest increases with 56.9% and 51.1% respectively, and alcohol and

tobacco and meat and fish the lowest changes with 9.9% and 14.1%.

34

Real prices were obtained by deflating nominal prices by the UBoS all items’ consumer price index (2005/06=100) to take account of potential changes in the purchasing power of Ugandan households. Prices are set at cluster/district level using the Deaton’s approach (1988).

Essay II

54

Table 2.3 presents both the food consumption shares (excluding leisure) and proportions of zero

consumption of commodity groups by panel round for rural and urban areas. What is apparent from

these figures are the disparities between rural and urban Ugandan households in the allocation of

their budgets to food and non-food items and among food commodities.

Table 2.3 Food consumption shares and proportion of zero consumption by commodity groups

UNPS-2006 UNPS-2010 UNPS-2011

Rural Urban

Rural Urban Rural Urban

Mean Zeros Mean Zeros Mean Zeros Mean Zeros Mean Zeros Mean Zeros

Food 0.637

(0.198)

- 0.454

(0.204)

- 0.629

(0.217)

- 0.431

(0.199)

- 0.692

(0.203)

- 0.504

(0.214)

-

1k 0.093

(0.151)

0.596 0.099

(0.127)

0.453 0.099

(0.153)

0.575 0.105

(0.130)

0.439 0.111

(0.167)

0.560 0.109

(0.128)

0.389

2k 0.111

(0.151)

0.393 0.044

(0.089)

0.573 0.115

(0.146)

0.340 0.051

(0.090)

0.530 0.085

(0.134)

0.536 0.031

(0.077)

0.715

3k 0.095

(0.143)

0.470 0.046

(0.084)

0.536 0.099

(0.140)

0.412 0.053

(0.089)

0.450 0.028

(0.092)

0.850 0.011

(0.052)

0.923

4k 0.100

(0.094)

0.360 0.078

(0.109)

0.317 0.110

(0.157)

0.376 0.085

(0.120)

0.288 0.086

(0.139)

0.449 0.069

(0.103)

0.334

5k 0.088

(0.099)

0.239 0.066

(.070)

0.222 0.096

(0.109)

0.243 0.074

(0.090)

0.224 0.117

(0.140)

0.241 0.080

(0.096)

0.212

6k 0.149

(0.145)

0.278 0.176

(0.137)

0.195 0.144

(0.145)

0.311 0.173

(0.141)

0.209 0.175

(0.171)

0.286 0.189

(0.141)

0.170

7k 0.101

(0.094)

0.066 0.090

(0.067)

0.076 0.104

(0.096)

0.071 0.096

(.148)

0.068 0.097

(0.100)

0.084 0.093

(0.081)

0.063

8k 0.032

(0.034)

0.030 0.039

(0.036)

0.067 0.032

(0.032)

0.039 0.037

(0.033)

0.053 0.038

(.067)

0.034 0.041

(0.037)

0.055

9k 0.033

(0.075)

0.670 0.033

(.080)

0.748 0.028

(0.071)

0.722 0.019

(.073)

0.840 0.036

(0.089)

0.710

0.024

(0.077)

0.830

10k 0.197

(0.187)

0.101 0.329

(0.237)

0.020 0.174

(0.184)

0.122 0.307

(0.067)

0.027 0.225

(0.213)

0.094 0.352

(0.234)

0.028

Sample 1818 492 1823 487 1804 506

Note: Item indices ik : 1: Matooke; 2: Cassava; 3: Potatoes; 4: Maize; 5: Beans; 6: Meat and fish; 7: Fruits and

vegetables; 8: Fats and oils; 9: Alcohol and tobacco ; and 10: Other foods. Standard deviations into brackets.

By and large, rural households, predominately agricultural, have allocated to food items 41% more

of their budget than urban households whose shares of food consumption in total expenditures

counted for around 46%. Between the first and the last surveys, food consumption shares rose for

both rural and urban households by 8.6 and 11%, respectively, due particularly to substantial

increases between 2009/10 and 2010/11 (10% and 16.9% in rural and urban areas, respectively),

while between 2005/6 and 2009/10 food consumption shares slightly decreased for both rural and

urban households (1.3% and 5.1%, respectively).


55

Out of the food consumption, the consumption shares of different food items are relatively close

(around or less than 10%), except for meat & fish and other foods which shares are on average

greater than 15%. This may suggest that the Ugandan diet is particularly diversified and thus there

might be large possibilities of substitution across commodities as a response to food price increases.

When we compare the dynamics of these shares during the sample period, beans (32.9% and 21.2%

in rural and urban areas, respectively), matooke (19.4% and 10.1%), and meat & fish (17.4% and

7.4%) displayed the highest increases in their consumption shares between 2005/6 and 2010/11,

while potatoes (-70.5% and -76.1%), cassava (-23.4% and -29.5%), and maize (-14% and -11.5%)

had the highest decreases.

When we disaggregate these total changes into the two sub-periods, it appears that for both rural

and urban households, most consumption shares showed larger changes (in absolute values) in the

first sub-period (2005/6 – 2009/10) than in the second (2009/10- 2010/11) . In the first sub-period,

the shares increased on average by 28.9 and 3.5% for rural and urban households, respectively,

whereas during the last sub-sample period, they rose in rural areas (+1.4%) but decreased for urban

households (-4.6%). Finally, the proportion of zero consumption is relatively high for all food

groups, except for fruits & vegetables, fats & oils, and other foods. This underscores the need to

explicitly deal with the censoring issue when estimating the food demand systems.

2.4.3 Identification of the household’s food market position

In addition to the assumption that the welfare effects of price changes are significantly different

under separable and non-separable models, we also assume that these effects are likely to be

different across households due to their heterogeneity in terms of food market position. As outlined

in our conceptual framework, frictions in the labor markets (whether due to risks, transaction costs,

or imperfect substitutability between different types of labor) introduce into the model virtual or

shadow effects of food price changes which signs and magnitudes are a priori indeterminate. These

additional effects will either over- or under-estimate the expenditure and price elasticities and,

consequently, the welfare effects of price changes derived under the recursivity hypothesis,

depending on the extent of the household’s net positions in both the food and labor markets (see

equation 2.15). To take account of this fact, households are first divided into non-agricultural and

agricultural households. The former act as pure consumers of staple foods and their welfare effects

are theoretically the same in both separable and non-separable models, while the latter produce

foods that are either consumed or sold, or both. Second, for each agricultural household, the net

market position (or market surplus/deficit) is defined as the difference between the total market

Essay II

56

value35

of quantities sold )( 1A and quantities purchased )( 2A of key staple foods consumed and

produced by Ugandan households, namely matooke, maize, potatoes, cassava, beans, rice, millet,

sorghum, fruits & vegetables. Hence, a household is defined as a global net seller (buyer) if 1A

)( 2A . Moreover, among net sellers, significant net sellers are those with 21 *5.1 AA while

insignificant or marginal net sellers are characterized by 212 *5.1 AAA . A similar subdivision is

applied to net buyers. This profiling of the net market status of households using the value

definition – instead of weight definition, for example – is particularly suitable in the context of this

study as it provides greater insight on households’ vulnerability to unexpected price changes by

incorporating information on both prices and quantities of staples sold and purchased. Furthermore,

this disaggregation will shed light on whether differences in market surplus/deficit led to significant

differences in the welfare impacts of price changes as outlined in the theoretical framework.

Summary statistics and descriptions of key variables used in the estimation of different models are

reported in table 2.4 by survey round and net market position. The table depicts significant

discrepancies among the different types of households in terms of the dynamics of key variables of

interest, hence highlighting the need to profile households through their net market position.

Unsurprisingly, non-agricultural households (column A) present the highest monthly real

expenditures per adult equivalent both in terms of food purchases (vcmarket) and non-food

expenditures (vnctotal), with respectively an average over the sample period of 43,400 and 81,500

Uganda Shillings (UShs)36

. While the total household expenditures (tothexp2) excluding non-

purchased foods (imputed values of consumption from home production, vcproduce, and

consumption of food received in-kind or as gifts) have decreased over time by 10.9% between the

first and second surveys (henceforth, the first sub-period) and by 32.3% between the second and last

surveys (the second sub-period), non-agricultural households increased their expenditures on food

items (vcmarket), and particularly of staple foods (vcmarketstaples) in the first sub-period. Hence,

when taken together, food purchases rose by a modest 2.2% during that period, but expenditures on

staples soared on average by 66.7%, before declining afterwards by 16.8%. These dynamics provide

some insights on the possible reallocation of households’ budget between food and non-food items.

During periods of high and volatile prices, pure consumers are generally found to decrease their

expenditures on non-food items such as health and education to smooth their consumption

35

To check for the robustness of our results, we also applied different definitions of the net market position, using for example the values of harvest instead of values of sales and the values of consumption instead of purchases (net producers vs net consumers). 36

Average nominal exchange rate between May 2005 and April 2006 (first survey coverage): 1USD = 1,809.9 Uganda Shillings; between September 2009 and August 2010 (second survey): 1USD = 2,054.4 UShs; and between October 2010 and September 2011 (third survey): 1USD = 2,441.3 UShs (Bank of Uganda, 2013)


57

(Hoddinott, 2006; Carter et al., 2007). Finally, the table shows that non-agricultural households are

likely to have lower family size, younger heads with more years of education and are predominately

male-headed.

Significant net sellers (column B) logically spent the least on food consumption with a real monthly

average per adult equivalent of less than 10,000UShs. However, they followed the same dynamics

as non-agricultural households in terms of expenditures of staple foods: first an increase (of 62.5%)

between 2005/6 and 2009/10 and then a decrease (of 42.3%) during the second sub-period. This

feature is recurrent among other agricultural households, although occurring at different growth

rates. Significant net sellers are also characterized by the highest levels of crops harvested and sold

which, compared to relatively stable expenditures on variable inputs (vinputs: seeds, pesticides,

fertilizer, and costs of hired labor), yielded the highest farm profits in each survey round. However,

while most indicators present a positive growth rate between the first and second surveys,

significant net sellers recorded a striking drop during the second sub-period, particularly in regards

to quantities harvested (-56.6%), sold (-55.5%), and farm profits (-64.5%). Several reasons may

explain these figures, among them the relatively modest increases in real food prices (21.4% against

139.4% in the first sub-period) that may have incited farmers to engage in alternative activities

(non- or off-farm employment) that became more profitable. This can be seen by the decreases in

the land size allocated to crops (-36.9%), the number of crops grown (-18.6%), on-farm family

labor (-3.7%), and hired labor (-61.1%), but increases in off-farm labor (+67.2) or non-farm income

(+58.1%).

At the opposite side of significant net sellers, significant net buyers (column C) have the highest

levels of food purchases. Although they both have relatively similar levels of total values of food

consumption (vctotal), and non-food (vnctotal), food expenditures of significant net buyers exceed

that of significant net sellers on average by 82.4, 74.7, and 87.7% in each survey round,

respectively. Further, they harvested and sold the least, yielding the lowest farm profits (even

experiencing a net loss in 2010/11). They also cultivated the lowest proportion of land (on average

2.52 acres), grew less crops (around 4), allocated less time to on-farm family labor and much of

their time to off-farm labor. Their heads are on average relatively older and the least educated. Put

together, these features make significant net buyers particularly at the mercy of instabilities in

commodity price markets. As shown in the table, they are selling food crops (vsalestaples) even

when their harvest might be insufficient to cover their consumption needs. And given that farmgate

prices are generally lower than consumer prices due to high transaction in most developing

countries, they end up selling at low prices during harvested seasons but buying at high market

prices at the lean periods.

Essay II

58

Table 2.4 Household characteristics by year and net market position

Variable

labels

All A B C D E

2006 2009 2010 2006 2009 2010 2006 2009 2010 2006 2009 2010 2006 2009 2010

vcmarket (a) 19.4

(24.3)

45.6

(45.9)

46.6

(39.9)

38.4

(33.8)

10.2

(11.4)

9.1

(11.2)

8.1

(10.5)

18.6

(17.9)

15.9

(14.9)

15.2

(14.4)

13.5

(12.1)

12.5

(8.3)

13.1

(10.9)

14.5

(15.8)

15.4

(11.6)

11.7

(10.9)

vcmarketstaples(a) 9.8

(12.7)

15.7

(13.2)

26.2

(20.1)

21.8

(19.8)

1.6

(2.5)

2.6

(4.1)

1.5

(2.9)

8.8

(10.3)

11.1

(10.8)

9.7

(10.5)

4.4

(4.5)

6.2

(4.9)

4.6

(4.5)

4.9

(5.2)

8.4

(7.6)

5.1

(5.7)

vcproduce(a) 10.8

(12.8)

- - - 19.5

(15.5)

18.2

(12.3)

14.4

(12.1)

11.5

(13.8)

11.6

(12.1)

9.5

(9.8)

17.2

(21.8)

16.4

(9.6)

14.7

(10.9)

16.2

(12.3)

18.7

(13.6)

17.1

(13.1)

vctotal(a) 32.9

(26.7)

51.1

(45.8)

52.5

(42.4)

44.8

(33.9)

31.3

(20.4)

29.1

(17.3)

25.2

(16.9)

32.1

(25.9)

29.8

(19.2)

26.6

(17.9)

31.9

(27.7)

31.1

(17.4)

33.1

(37.2)

32.1

(23.2)

35.7

(19.2)

30.7

(32.7)

vnctotal(a) 31.7

(162.4)

105.5

(625.2)

88.1

(95.3)

52.8

(61.6)

22.6

(26.3)

24.6

(36.5)

13.7

(21.1)

22.9

(36.2)

24.1

(54.4)

15.3

(34.3)

28.3

(34.5)

23.7

(24.8)

14.1

(21.8)

26.2

(34.6)

30.1

(27.2)

18.3

(25.5)

tothexp1(a) 64.7

(168.8)

156.6

(630.9)

140.5

(121.4)

97.6

(84.5)

53.9

(38.9)

53.6

(42.9)

38.9

(30.3)

54.9

(52.5)

53.8

(61.1)

41.9

(42.3)

60.3

(50.1)

54.9

(34.3)

47.1

(45.1)

58.4

(47.4)

65.7

(35.8)

48.9

(36.7)

tothexp2(a) 51.1

(168.9)

151.1

(631.3)

134.7

(120.2)

91.2

(85.2)

32.7

(32.9)

33.6

(41.1)

21.7

(26.8)

41.5

(47.8)

40.1

(60.6)

30.5

(41.3)

41.8

(42.9)

36.2

(29.1)

27.2

(27.7)

40.8

(43.1)

45.3

(32.2)

30.1

(32.7)

vharvest(a) 397

(746)

- - - 1,061

(1,179)

1,009

(1,206)

438.1

(449.5)

318.9

(519.8)

122.6

(319.9)

84.8

(233.1)

898.4

(1,061)

524.8

(468.1)

347.9

(394.5)

699.4

(778.1)

559.9

(542.9)

366.2

(519.9)

vharveststaples(a) 306

(559)

- - - 855.5

(883.3)

815.6

(908.1)

361.6

(449.5)

244.7

(344.8)

67.5

(147.7)

50.1

(125.6)

654.9

(702.9)

437.9

(420.3)

290.4

(324.1)

557.8

(566.9)

424.8

(399.6)

306.7

(438.3)

vsales(a) 197

(421)

- - - 506.9

(664.7)

626.3

(727.2)

278.8

(345.2)

76.5

(208.7)

67.7

(147.7)

45.2

(125.4)

403.1

(564.4)

398.7

(299.6)

215.6

(188.1)

273.3

(455.4)

325.1

(361.6)

172.3

(192.9)

vsalestaples(a) 137

(323)

- - - 385.9

(534.6)

502.3

(604.5)

221.6

(267.2)

28.5

(68.2)

28.1

(61.8)

21.5

(58.8)

240.1

(355.9)

218.9

(223.3)

173.1

(164.2)

164.6

(261.3)

201.4

(164.7)

129.9

(157.6)

vinputs(a) 25

(102)

- - - 101.3

(262.8)

120.9

(215.8)

96.9

(181.9)

42.8

(242.1)

49.9

(162.4)

51.5

(107.2)

130.1

(372.2)

81.1

(134.7)

110.7

(214.6)

76.9

(188.3)

124.3

(195.7)

113.3

(251.4)

frprofit(a) 130

(386)

- - - 398.9

(560.3)

513.1

(643.9)

181.8

(301.8)

29.5

(264.9)

24.3

(237.7)

-6.2

(130.4)

301.5

(551.9)

220.1

(267.9)

104.9

(239.6)

218.8

(421.8)

203.5

(316.6)

59.1

(215.6)

land 3.62

(14.90)

- - - 3.63

(3.45)

4.33

(8.29)

2.73

(4.03)

1.98

(3.12)

2.95

(11.8)

2.61

(8.10)

3.89

(4.06)

2.64

(6.18)

2.97

(1.78)

2.49

(4.15)

2.89

(4.41)

2.89

(4.93)

ncrops 4.79

(3.22)

- - - 6.56

(2.93)

6.83

(3.79)

5.56

(3.35)

3.64

(2.66)

4.00

(3.08)

4.36

(2.78)

4.95

(2.52)

6.09

(3.15)

6.49

(3.11)

5.03

(2.84)

5.55

(2.77)

6.80

(3.54)


59

Table 2.4 (continued)

Variable

labels

All A B C D E

2006 2009 2010 2006 2009 2010 2006 2009 2010 2006 2009 2010 2006 2009 2010

onflabor 3,118

(5,641)

- - - 4,221

(3,819)

4,342

(13,794)

4,180

(5,882)

1,862

(2,508)

2,413

(3,164)

3,312

(3,673)

2,712

(3,146)

3,963

(5,081)

3,207

(2,657)

2,747

(2,777)

3,278

(3,318)

3,086

(3,561)

hlabor 24.72

(289.61)

- - - 165

(534)

329

(717)

128

(356)

138

(808)

291

(4,886)

124

(338)

419

(1,119)

311

(1,829)

143

(365)

320

(804)

239

(607)

66

(183)

offlabor 1,215

(3,431)

- - - 1,032

(3,438)

807.8

(3,917)

1,351

(2,633)

1,819

(3,919)

1,315

(3,798)

754.8

(2,546)

1,234

(3,619)

1,214

(2,958)

640.4

(1,805)

2,057

(4,161)

806.7

(2,861)

1,133

(2,978)

nonfincome(a) 384.1

(1,058)

1,284

(1,872)

300.6

(1,076)

461.5

(1,248)

212.9

(789.7)

200.1

(769.4)

316.3

(697.5)

548.9

(1,235)

215.9

(776.5)

273.9

(803.5)

481.8

(1,322)

277.3

(970.1)

398.5

(1,217)

469.1

(935.1)

218.3

(8614)

282.1

(586.8)

hhsize 6.55

(3.36)

4.46

(2.88)

5.29

(3.11)

6.23

(3.66)

6.16

(3.22)

7 (3.36) 7.40

(3.50)

5.97

(2.86)

6.77

(3.17)

7.55

(3.44)

6.15

(3.02)

6.73

(3.46)

7.91

(3.69)

6.40

(3.31)

7.01

(3.23)

7.64

(4.34)

age 45.6

(15.1)

36.9

(12.6)

41.3

(13.8)

42.9

(14.2)

44

(14.78)

47

(14.28)

47.6

(14.89)

44.3

(15.58)

48.32

(15.20)

48.8

(14.99)

42.9

(14.9)

44.2

(13.9)

46.3

(14.11)

41.8

(14.19)

47.7

(16.1)

47.8

(14.98)

education 5.30

(4.10)

6.86

(4.35)

7.06

(4.62)

7.18

(4.83)

5.34

(3.51)

5.31

(3.64)

5.33

(3.85)

4.58

(3.88)

4.44

(3.98)

4.96

(4.09)

5.47

(3.31)

5.25

(3.48)

5.69

(3.34)

6.09

(3.48)

5.27

(3.52)

5.54

(3.94)

Gender 70.81 79.01 81.82 79.10 78.8 77.62 77.31 70.40 67.28 65.66 69.27 69.95 65.69 76.47 77.42 72.88

Observations 6,930 423 376 437 552 563 454 1,152 1,201 1,293 81 77 67 102 93 59

Note: (a) in ,000’s Uganda Shillings (UShs). Standard deviations into brackets. All monetary values are expressed in real terms using UBOS’ Consumer price index

(2005/6: Base=100). A represents non – agricultural households, B significant net sellers, C significant net buyers, D insignificant net sellers, and E insignificant net

buyers.

Variable labels: vcmarket: real monthly per adult equivalent (r.m.a., henceforth) total food consumption expenditures; vcmarketstaples: r.m.a. food consumption

expenditures of staples. vcproduce: r.m.a. values of food consumption from home production. vctotal: r.m.a total values of food consumption (sum of food

purchases, consumption from home production, and consumption in-kind or obtained as gifts); vnctotal: r.m.a. total household expenditures on non-food items

(education, health, durables, non- or semi-durable goods,…); tothexp1 and tothexp2 denote the r.m.a total household expenditures on food and non-food items,

including and excluding consumption from home-production vcproduce and food received in-kind or as gifts, respectively; vharvest (vharvestsaples): total annual

values of all crops (staples) harvested; vsales (vsalestaples): total annual values of all crops (staples) sold; vinputs: annual expenditures on variable inputs (seeds,

pesticides, fertilizer, hired labor); frprofit: farm profit; land: land size (in acres); ncrops: number of crops grown during the main season; onflabor: annual hours of

on-farm family labor ; hlabor: annual hours of hired labor; offlabor: annual hours of off-farm labor; nonfincome: real annual non-farm income; hhsize: household

size; age: age of the household head; education: number of years of education attained by the household head; and gender: proportion of male-headed households.

Essay II

60

In this context, if unexpected price increases occur during periods of low storage capacity and with

the lack of well-functioning credit and other financial markets, the risk of deterioration of welfare

conditions becomes increasingly high.

Between significant net sellers and buyers appear both marginal net sellers and buyers. They both

spend relatively similar amount of money on food consumption, higher than significant net sellers

but lower than significant net buyers. Their discrepancies become apparent when we look at the

production side. Insignificant net sellers (column D) produced on average more than insignificant

net buyers (+6.3%) only due to the 2005/6’s harvest levels (+28.5%). When we only take account of

the last two surveys, the picture becomes reversed, with insignificant net buyers (column E)

producing and selling globally more than insignificant net sellers, although net sellers are still

selling more staples than net buyers (+18.8%). Other important differences between these two sub-

groups are related to the levels of farm profits, hired labor, or time spent on off-farm employment.

Hence, the above analyses of household characteristics disaggregated by their net position in the

food market provide the following key messages that will become apparent in the subsequent

sections. First, treating all households as a homogenous group is likely to result in a misleading

picture of the dynamics occurring among them. One evidence of this is that food purchases of non-

agricultural households are for instance at least 2 times higher than the overall average food

expenditures (second column). Second, decomposing agricultural households between net sellers

and net buyers still hides important heterogeneity in terms of consumption, production, and other

household characteristics. Ideally, given the complexity of agricultural households’ behavior (Singh

et al., 1986; Strauss, 1986; de Janvry and Sadoulet, 1991; Key et al., 2001), one would need to build

as many homogenous sub-groups as data allow. Since different sub-groups of agricultural

households will certainly be diversely affected by food price changes, depending on their initial

conditions, observable characteristics, and unobserved heterogeneity, group-specific targeted policy

interventions are likely to be more effective than uniform policies.

To conclude these data descriptions, we report in table 2.5 the number of agricultural households by

their net positions in both food and labor markets. Among the 5,694 total agricultural households,

the majority (2,670 or 46.89%) is either self-sufficient ( 0 hfLL ) or autarkic ( 0 hf

LL ) in the

labor market. Labor net buyers ( 0 hfLL ) slightly outweigh net sellers ( 0 hf

LL ) with 28.96

against 24.15%. For all types of agricultural households, around three-quarters are labor net buyers,


61

self-sufficient, or autarkic. Referring to equation (2.10)37

and table 2.1, this implies that for the

majority of the surveyed households, both the price elasticities and compensating variations are

theoretically indeterminate in the non-separable model.

Table 2.5 Decomposition of Ugandan households by their net positions in the food and labor markets

Labor net sellers: 0 hfLL Labor net buyers: 0 hf

LL Self-sufficient/Autarkic:

hfLL

Total 2005/6 2009/10 2010/11 Total 2005/6 2009/10 2010/11 Total 2005/6 2009/10 2010/11

B 314 116 115 83 543 297 133 113 712 139 315 258

C 946 428 256 262 949 349 245 355 1,751 375 700 676

D 45 18 18 9 40 40 18 22 100 23 41 36

E 70 38 16 16 38 38 30 9 107 26 47 34

Total 1,375 600 405 370 1,649 724 426 499 2,670 563 1,103 1,004

Note: B represents significant net sellers, C significant net buyers, D insignificant net sellers, and E

insignificant net buyers.

2.5 Results and discussion

2.5.1 Estimation of shadow wages and separability test

Parameter estimates for both the stochastic production frontier function hthtXF , and technical

inefficiency htU are reported in tables 2.6 and 2.7. The empirical functional form of the production

frontier function is represented by a flexible quadratic specification in the productive assets38

.

Although displayed in two distinct tables, both models were estimated simultaneously using the

Battese and Coelli’s (1995) Maximum Likelihood-random effects time-varying inefficiency effects

model. Globally, the estimated coefficients have the expected signs. All labor and non-labor inputs

statistically significantly increase the values of crops harvested39

. For instance, increases in the

quantity of on-farm family female labor appear to have more impact on the marketed values of

harvests than male labor. Hence, activities such as weeding or transplanting, generally executed by

women in Uganda, would tend to be more important to the overall production than for example

37

For self-sufficient or autarkic households in the labor market, equation (2.10) reduces to:

a

Hff

faaa

Hfaf pwEwcEYcE

Y

cQppcEpcE **////

38 We also used other functional forms of the production frontier hthtXF , such as a generalized Leontief

functional form given the preponderance of zero values in input uses. However, only the model presented in this study best fitted the data while others fail to converge or present unrealistic parameter estimates. 39

For each variable, we run joint tests of the level, quadratic, and interaction terms included in the final empirical specification.

Essay II

62

ploughing in which men are predominantly engaged (Jacoby, 1993; Abdulai and Regmi, 2000;

Tiberti and Tiberti, 2012).

Table 2.6 Stochastic production frontier estimates

Dependent variable: Total value of quantity harvested (in log)

Coefficients Standard errors

Constant 11.805 0.202

land 0.863 0.097***

onfmalelabor 0.181 0.080**

onffemalelabor 0.235 0.061***

onfchildlabor 0.040 0.056

hlabor 0.055 0.024*

varinput 0.193 0.025***

wagehlabor 0.043 0.044

½ land2

-0.227 0.046***

½ onfmalelabor2

0.054 0.030**

½ onffemalelabor2

0.074 0.022**

½ onfchildlabor2

0.037 0.024

½ hlabor2

0.096 0.020***

½ varinput2

0.055 0.004***

½ ghiredlabor2

0.021 0.008***

Land × onfmalelabor 0.091 0.034***

Land × onffemalelabor -0.051 0.039

Land × onfchildlabor 0.057 0.031*

Land × hlabor -0.005 0.028

Land × varinput 0.006 0.010

Land × wagehlabor -0.028 0.011**

onfmalelabor × onffemalelabor -0.086 0.027***

onfmalelabor × onfchildlabor 0.017 0.023

onfmalelabor × hlabor -0.080 0.032**

onfmalelabor × varinput 0.003 0.008

onfmalelabor × wagehlabor -0.005 0.011

hlabor × varinput -0.004 0.006

hlabor × wagehlabor -0.017 0.007***

LqGood 0.217 0.085**

LqFair 0.062 0.086

LdIr -0.128 0.177

Yr2009 0.222 0.008***

Yr2010 0.182 0.108*

v 0.343 0.043

u 0.737 0.018

222 / vuu 0.827 0.015

Observations 5,694

Note: All continuous variables are reported in log. ***

, **

, and * denote statistical significance at 1, 5, and 10%

levels, respectively.

Variable labels: land: land size (in acres); onfmalelabor, onffemalelabor, and onfchildlabor : on-farm family

labor (in person-days) by adult males, adult females, and children, respectively; hlabor: hired labor (in person-

days); varinput: total expenditures on seeds, pesticides, and fertilizer used for production; wagehlabor: costs of

hired labor. LqGood: proportion of plots of good quality; LqFair: proportion of plots of fair quality; LdIr:

proportion of irrigated plots; Yr2009 and Yr2010: dummy variables taking 1 if year=2009 and 2010, respectively.


63

Table 2.7 Technical inefficiency estimation results

Coefficients Standard errors

Constant 0.365 0.051***

Gender 0.047 0.003***

Age -0.006 0.001***

Age2

0.000 0.000***

Education: Primary level -0.103 0.008***

Secondary -0.094 0.010***

University -0.132 0.030***

Number of crops grown 0.012 0.002***

Number of crops grown2

-0.001 0.000***

Married 0.063 0.007***

Number of children -0.005 0.001***

adult male -0.013 0.002***

adult female -0.021 0.002***

Eastern region 0.047 0.042

Northern region 0.014 0.043

Western region 0.124 0.040***

Ratio Labor/Land 0.006 0.001***

Ratio Adult labor/Total labor 0.109 0.007***

Observations 5,694

Note: ***

and **

denote statistical significance at 1 and 5% levels.

Jointly, family labor is found more productive than hired labor which highlights the possibility of

imperfect substitutability between these two types of labor due for instance to the existence of

supervision costs or differential work motivations (Deolalikar and Vijverberg 1987). Land

characteristics also clearly influence the crop outputs, which values are statistically higher with

increases in land size, when cultivated lands are of good or fair quality. The costs of non-labor

inputs (seeds, pesticides, and fertilizer) and hired labor positively influenced the output values,

though only marginally when compared with the joint effect of family labor. This is probably

imputable to their limited usage by Ugandan farmers during the sample period40

.

In terms of technical inefficiency, table 2.7 reveals that its scores are significantly correlated with

the gender, level of education of the head and his marital status as well as with household

composition, regional effects, and labor-land ratio.

Once we get the estimated parameters from the stochastic production frontier and technical

inefficiency, we can derive sequentially the estimated marginal product revenue of labor for the

entire sample LPRM ˆ , compute the allocative inefficiency scores for farmers engaged in both on- and

off-farm labor IA ˆ , and finally obtain the estimates of the shadow wages *w for households that did

not supply labor to the market. Following the procedure outlined previously (see section 2.3.1), we

40

For instance, only 3.86, 5.57, and 5.20% of Ugandan farmers use fertilizer (either chemical or organic) in each survey round, respectively. The proportion that purchased pesticides was relatively high, with 11.92, 14.72, and 14.56%, respectively.

Essay II

64

summarize in table 2.8 these different values for the full sample, the sub-sample of off-farm

workers and self-employed farmers. Theoretically, the allocative inefficiency condition should hold

( wPRM L ˆ ) for agricultural households supplying labor off-farm. Descriptive statistics reported in

table 2.8 indeed reveal that the mean observed market wages of farmers working off-farmers only

slightly deviate from their estimated marginal product revenue of labor. And as expected, the LPRM ˆ

of self-employed farmers is on average 22% higher than that of households working off-farm. The

consequence of these small deviations between the mean LPRM ˆ and observed market wages for

farmers supplying labor is that their allocative inefficiency scores will tend to approach small values

while they will be higher, in absolute values, for self-employed agricultural households. Negative

(positive) IA ˆ will thereby imply that farmers are undersupplying (oversupplying) on-farm labor

relative to off-farm employment (Barrett et al., 2008). As shown in table 2.8, self-employed,

contrarily to off-farm workers, tended to undersupply on-farm labor (they reported on average

negative estimated IA ˆ scores). Finding similar results when using data from rice production in Cote

d’Ivoire, Barrett et al. (2008) attributed this empirical evidence to labor constraints that impede self-

employed agricultural households from working off-farm since they do not have sufficient labor to

operate on their own farms.

Table 2.8 Summary statistics for w , LPRM ˆ , IA ˆ , and *w

w LPRM ˆ IA ˆ *w

observations

Full sample - 815.95

(125.05)

-0.16

(0.25)

1,073.14

(636.23)

5,694

Off-farm workers 787.31

(582.07)

751.62

(115.97)

0.05

(0.23)

787.31

(582.07)

2,675

Self-employed

farmers

- 916.19

(50.56)

-0.21

(0.20)

1,520.65

(424.27)

3,019

Note: w : Observed real hourly market wage, at the community level ; LPRM ˆ : Estimated real marginal

product revenue of labor; IA ˆ : Estimated allocative inefficiency score; *w : Estimated hourly shadow wage.

Standard deviations into brackets

Furthermore, table 2.8 indicates that the mean values of estimated shadow wages are clearly larger

than observed market wages, as predicted by the non-separable agricultural households’ literature.

Thus, the observed market wages w serve as lower bounds of the farmers’ subjective valuation of

their on-farm labor. Finally, as a simple separability test, we performed both the Kolmogorov-

Smirnov (K-S) and Epps-Singleton (E-S) tests for equality of shadow wages’ distributions between


65

the sub-samples of off-farm workers and self-employed farmers41

. With both tests reporting p-

values of zero, we reject the null hypothesis of equal distributions of estimated shadow wages and

observed market wages. Otherwise stated, these results suggest that addressing the unobserved

wage problem of agricultural households not supplying labor to the market by using observed

market wages would underestimate the true, though unknown, cost of on-farm labor and

consequently would bias subsequent welfare analyses.

2.5.2 Demand elasticities

Expenditure and Hicksian own-price elasticities42

are reported in tables 2.9 and 2.10 for both

separable43

and non-separable models to evaluate the extent of virtual or shadow effects on

household consumption behavior. All sets of elasticities are computed at the mean values of the

predicted consumption shares and controlled for censoring in food consumption. To account for

both year-specific effects and households’ heterogeneity in regards to their net position in the food

market, these elasticities are shown by survey round and net seller/net buyer status.

Conditional expenditure elasticities

As expected, all expenditure elasticities ( i ) are found positive and significant at 1% level,

implying that increases in households’ overall values of food consumption are accompanied with

increases in demand of the individual food items under consideration. In the separable models, meat

& fish ( 6 ) and other foods ( 9 ) display elasticities greater than one, suggesting that they are

luxuries for Ugandan households: as income increases, households will spend proportionally more

on the consumption of these food items. Furthermore, compared to food items, estimated elasticities

associated with leisure are the lowest, with a 1% increase in household’s total expenditure leading

to less than 0.6% increase of time allocated to leisure. This could be a reflection of labor constraints

faced by Ugandan households, predominately rural and agricultural. The rural labor market is

structurally thin and characterized by limited employment opportunities and lower wage rates. In

this context, the household’s time endowment is often allocated to leisure by default and many

41

Both the K-S and E-S tests check for dissimilarities between two samples by comparing either their distribution functions (K-S tests) or their empirical characteristic functions (Epps and Singleton, 1986; Goerg and Kaiser, 2009). 42

Theoretical restrictions of adding-up and symmetry were imposed to the model and the system of share equations in the QUAIDS was estimated using the Non-linear Seemingly Unrelated Regression (NSUR) suggested by Poi (2008). Expenditure endogeneity has been tested and controlled for as well as censoring due to zero purchases using the Shonkwiler and Yen (1999)’s approach. Household composition (number of children, male, and female adults), total time endowment, non-farm incomes, sex, education and age of the head, and consumer prices were used as instruments of the shadow value of leisure in the non-separable model.

43 See Appendix B.2 for the expressions of demand elasticities from the QUAID model under separability.

Essay II

66

households would promptly decrease its share had they received employment offers. In terms of

year-specific effects, expenditure elasticities have increased for most food items between 2005/6

and 2009/10 before decreasing in the last survey round. Otherwise stated, periods of higher food

price volatilities were characterized by higher sensitivity of Ugandan households to changes in their

total expenditures.

When disaggregating households by their food net market status, it appears that differences in

estimated expenditure elasticities are particularly striking between significant net sellers and

significant net buyers, at least for food items included in the definition of the net seller/net buyer

position. Significant net buyers are found to increase the consumption of food items on average by

13% more than their net seller counterparts, with the highest differences related to matooke

%)31( 1 and beans %)33( 5 . This is easily understandable since significant net buyers are

conceptually in a more urgent need to cover their food deficit than significant net sellers or other

agricultural households. By contrast, it is hard to clearly perceive the disparities between

insignificant net sellers and net buyers. For most food items, their corresponding estimated

expenditure elasticities are remarkably close. Except for matooke %)17( 1 and beans

%)14( 5 , their differences barely reach 1%. Non-agricultural households lie somehow between

these sub-groups of agricultural households. For example, they are increasing the consumption of

most food items more proportionally than significant net sellers but are relatively closer to

significant net buyers than to insignificant net sellers or net buyers.

When we relax the assumption of perfect labor markets and impute the value of leisure using

shadow wages in lieu of observed market wages, all estimated expenditure elasticities are still

positive and significant at 1% level but their magnitude is now reduced for most food items and

household sub-groups. Analytically, the discrepancy between separable and non-separable models

is attributed to the combined effects of the cross-price elasticities of the shadow wages */ wcE i

and the elasticities of the shadow wages with respect to expenditures xwE /* 44. As reported in

Appendix B.3, these combined effects were negative for most households which therefore

underestimated the elasticities obtained with no labor market failures.

44 In the non-separable model, **

*

* **

/ wcExwExcExcEx

w

w

c

x

c

x

ciwii

i

w

ii


67

Table 2.9 Expenditure elasticities by survey round, net market position, and (non-) separability

2005/6 2009/10 2010/11 Net market position (pooled sample)

A B C D E

a. Separable model (Perfect labor market)

1 0.980

(0.023)***

0.995

(0.023)***

0.987

(0.024)***

0.944

(0.027)***

0.777

(0.016)***

1.022

(0.029)***

0.844

(0.016)***

0.989

(0.017) ***

2 0.903

(0.021)***

0.953

(0.021)***

0.969

(0.034)***

0.926

(0.060)***

0.954

(0.023)***

0.984

(0.021) ***

0.948

(0.024)***

0.942

(0.021) ***

3 0.908

(0.022)***

1.001

(0.022)***

0.970

(0.087)***

1.013

(0.022)***

0.892

(0.083)***

1.054

(0.029) ***

0.989

(0.023)***

0.985

(0.025) ***

4 0.859

(0.022)***

0.880

(0.021)***

0.884

(0.031)***

0.869

(0.028)***

0.783

(0.033)***

0.917

(0.021) ***

0.876

(0.025)***

0.875

(0.022) ***

5 0.729

(0.019)***

0.756

(0.019)***

0.704

(0.019)***

0.792

(0.016)***

0.588

(0.032)***

0.783

(0.018) ***

0.772

(0.017)***

0.663

(0.016) ***

6 1.214

(0.015)***

1.342

(0.015)***

1.244

(0.015)***

1.273

(0.016)***

1.236

(0.014)***

1.364

(0.015) ***

1.278

(0.012)***

1.297

(0.013) ***

7 0.886

(0.014)***

0.892

(0.014)***

0.874

(0.018)***

0.870

(0.017)***

0.873

(0.019)***

0.892

(0.014) ***

0.869

(0.017)***

0.888

(0.014) ***

8 0.866

(016)***

0.873

(0.017)***

0.856

(0.017)***

0.867

(0.019)***

0.850

(0.016)***

0.892

(0.016) ***

0.875

(0.017)***

0.874

(0.016) ***

9 1.234

(0.014)***

1.398

(0.015)***

1.242

(0.014)***

1.412

(0.017)***

1.249

(0.009)***

1.357

(0.016) ***

1.248

(0.018)***

1.206

(0.017) ***

10 0.978

(0.036)***

0.917

(0.047)***

0.920

(0.043)***

0.997

(0.044)***

0.917

(0.045)***

0.932

(0.040) ***

0.941

(0.018)***

0.944

(0.044) ***

11 0.579

(009)***

0.526

(0.011)***

0.551

(0.010)***

0.578

(0.011)***

0.588

(0.009)***

0.536

(0.010) ***

0.529

(0.010)***

0.572

(0.010) ***

b. Non-separable model (imperfect labor market)

1 0.825

(0.003) ***

0.855

(0.002) ***

0.841

(0.003) ***

0.944

(0.027) ***

0.838

(0.002) ***

0.841

(0.002) ***

0.839

(0.008) ***

0.853

(0.011) ***

2 0.754

(0.007) ***

0.847

(0.005) ***

0.777

(0.007) ***

0.926

(0.060) ***

0.762

(0.007) ***

0.802

(0.004) ***

0.774

(0.013) ***

0.742

(0.019) ***

3 0.793

(0.006) ***

0.873

(0.005) ***

0.833

(0.011) ***

1.013

(0.022) ***

0.813

(0.006) ***

0.829

(0.005) ***

0.793

(0.023) ***

0.798

(0.024) ***

4 0.661

(0.008) ***

0.741

(0.009) ***

0.674

(0.008) ***

0.869

(0.028) ***

0.673

(0.009) ***

0.699

(0.006) ***

0.685

(0.022) ***

0.648

(0.023) ***

5 0.512

(0.010) ***

0.583

(0.009) ***

0.538

(0.008) ***

0.792

(0.016) ***

0.557

(0.010) ***

0.549

(0.006) ***

0.473

(0.036) ***

0.461

(0.029) ***

6 1.259

(0.018) ***

1.300

(0.019) ***

1.289

(0.021) ***

1.273

(0.016) ***

1.276

(0.021) ***

1.295

(0.014) ***

1.188

(0.038) ***

1.233

(0.033) ***

7 0.654

(0.006) ***

0.627

(0.006) ***

0.663

(0.008) ***

0.870

(0.017) ***

0.625

(0.009) ***

0.657

(0.005) ***

0.643

(0.016) ***

0.652

(0.018) ***

8 0.594

(0.007) ***

0.657

(0.007) ***

0.619

(0.006) ***

0.867

(0.019) ***

0.591

(0.009) ***

0.641

(0.005) ***

0.568

(0.028) ***

0.600

(0.020) ***

9 0.736

(0.046) ***

1.071

(0.061) ***

1.037

(0.071) ***

1.412

(0.017) ***

1.092

(0.076) ***

1.071

(0.046) ***

1.007

(0.119) ***

1.059

(0.078) ***

10 0.794

(0.006) ***

0.773

(0.009) ***

0.739

(0.007) ***

0.997

(0.044) ***

0.784

(0.008) ***

0.764

(0.005) ***

0.781

(0.024) ***

0.778

(0.019) ***

11 0.349

(0.018) ***

0.314

(0.022) ***

0.393

(0.019) ***

0.578

(0.011) ***

0.326

(0.022) ***

0.523

(0.015) ***

0.201

(0.056) ***

0.135

(0.046) ***

Note: i are conditional expenditure elasticities. Item indices: 1: Matooke; 2: Cassava; 3: Potatoes; 4: Maize; 5: Beans;

6: Meat and Fish; 7: Fruits and vegetables; 8: Fats and oils; 9: Other foods; 10: Alcohol and tobacco; and 11: Leisure.

The net market position is defined as previously: A represents non – agricultural households, B significant net sellers, C

significant net buyers, D insignificant net sellers, and E insignificant net buyers. (***

) denote significance levels at 1%.

Essay II

68

Economically, an increase in the shadow wage, which represents the opportunity cost of leisure

time, will have the usual negative substitution effects (leisure becoming virtually more expensive,

households substitute towards food items and away from leisure) and an ambiguous income effect.

Thus, the above results suggest that either the income effect was also negative (which reinforces the

negative substitution effects) or positive but not sufficiently high enough to more than offset the

negative substitution effects for most households.

Conditional Hicksian own-price elasticities

With regards to price elasticities, table 2.10 reports the conditional compensated (Hicksian) own-

price elasticities evaluated at the means of the data by net market position and labor market regime.

All own-price elasticities are negative and statistically significant at 5%, indicating that increases in

consumer prices of each commodity group led to reductions in the quantity demanded of the same

commodity. Similarly to expenditure elasticities, most price elasticities are less than unity which

suggests some rigidities in households’ demand responsiveness to price changes. Only livestock

products and fish are found price elastic. Own-price elasticities portrayed in table 2.10 can be

analyzed either by comparing periods of low (UNPS-2006) and high prices (UNPS-2010 and

UNPS-2011) or by contrasting household groups by their net market position and labor market

regime.

Starting with the separable models, households became more sensitive to price changes when we

move from periods of low and stable prices to those of high instabilities in commodity prices.

Particularly, own-price elasticities of matooke, maize, and meat & fish increased, in absolute terms,

by 13, 17, 22% between 2005/6 and 2009/10 (Tefera et al., 2012). In terms of net position in food

markets, non-agricultural households (column A) were more sensitive to price changes of maize,

potatoes, fish and meat, with the lowest elasticities (in absolute terms) for matooke and cassava

which are the most important contributive staples to daily caloric intakes in Uganda45

. Own-price

elasticities for agricultural households present a more heterogeneous pattern than expenditure

elasticities. Globally, significant net sellers (column B) are the least demand-responsive to changes

in food prices, particularly for staple foods. They decrease their consumption by 0.55, 0.60, and

0.51% in reaction to a 1% increase in the real prices of matooke, potatoes, and beans, respectively.

As shown by Finkelshtain and Chalfant (1991), farm income is generally positively correlated with

the prices of consumption goods and food production acts as an insurance value that partially

protects consumer-farmers from price fluctuations. This stabilizing role will be important the larger

45

Between 2000 and 2009, matooke and cassava were the first and second most important staples in terms of daily caloric intakes with respectively 17% and 13% of the total daily caloric intakes (FAO, 2009).


69

the food market surplus of a farmer. Hence, since high food prices are often accompanied with

higher revenues and consequently increased possibilities for additional consumption, significant net

sellers have more room for maintaining or reducing their consumption levels less proportionally

than other agricultural households46

.

At the extreme side, significant net buyers (column C) were relatively more sensitive to changes in

prices of most food items under consideration. In the short run, net buyers behave like pure

consumers or non-agricultural households to unexpected changes in food prices given the practical

impossibility to adjust or increase their output production and supply. The higher their food market

deficit, the more they are likely to react to price changes as non-agricultural households. As shown

in table 2.10, except for matooke and cassava, own-price Hicksian elasticities of significant net

buyers are only slightly different to those of non-agricultural households. Insignificant net sellers

(column D) and buyers (column E) are intrinsically close to each other in terms of sensitivity to

price changes. Their food market surplus/deficit is not sufficiently high/lower to benefit/suffer from

high food prices as significant net sellers/buyers. Globally, insignificant net sellers (buyers) are

found more (less) sensitive than significant net sellers (buyers) to changes in prices of most food

items. Similarly to expenditure elasticities, accounting for frictions in the labor markets reduces the

magnitude of most price elasticities.

Hence, labor market failures tend to rigidify households’ responsiveness in the food markets due to

the presence of virtual or shadow effects. These findings are consistent with widespread evidence

on agricultural household responses to market incentives when imperfections are accounted for. For

instance, studies by de Janvry et al. (1991) and Taylor and Adelman (2002) found significant

disparities in households’ reactions to price changes in markets with and without frictions, the

former generally reporting lower responses than the latter. These results also underscore the risk of

biased welfare estimates when we make the assumption of separability between production and

consumption decisions of agricultural households and, as a direct consequence, the welfare effects

of price increases would probably be over-estimated (at least in the present study) with evident

adverse consequences on policy implementations.

46

However, due to transaction costs more or less important in most developing countries, there is a wedge between producer or farmgate prices and consumer prices. Therefore, income growth rate consecutive to food price increases will generally be lower than growth rates of consumption expenditures.

Essay II

70

Table 2.10 Own-price Hicksian elasticities by net market position

2005/6 2009/10 2010/11 Net market position (pooled sample)

A B C D E

a. Separable model (Perfect labor market)

1 -0.635

(0.040)***

-0.732

(0.038) ***

-0.696

(0.035) ***

-0.642

(0.042) ***

-0.546

(0.027) ***

-1.026

(0.046) ***

-0.672

(0.027) ***

-0.784

(0.029) ***

2 -0.684

(0.048)***

-0.702

(0.044) ***

-0.678

(0.064) ***

-0.516

(0.119) ***

-0.632

(0.049) ***

-0.978

(0.043) ***

-0.598

(0.053) ***

-0.637

(0.047) ***

3 -0.894

(0.044)***

-0.779

(0.041) ***

-0.958

(0.149) ***

-0.784

(0.147) ***

-0.600

(0.043) ***

-0.764

(0.053) ***

-0.776

(0.046) ***

-0.617

(0.051) ***

4 -0.790

(0.062)***

-0.798

(0.055) ***

-0.788

(0.072) ***

-0.801

(0.129) ***

-0.693

(0.075) ***

-0.795

(0.054) ***

-0.785

(0.068) ***

-0.756

(0.061) ***

5 -0.514

(0.050)***

-0.500

(0.045) ***

-0.537

(0.040) ***

-0.427

(0.072) ***

-0.508

(0.039) ***

-0.621

(0.042) ***

-0.515

(0.042) ***

-0.531

(0.040) ***

6 -1.001

(0.030)***

-1.223

(0.030) ***

-1.119

(0.026) ***

-1.260

(0.026) ***

-1.014

(0.031) ***

-1.129

(0.029) ***

-1.003

(0.025) ***

-1.158

(0.027) ***

7 -0.668

(0.027)***

-0.760

(0.025) ***

-0.753

(0.028) ***

-0.743

(0.030) ***

-0.745

(0.030) ***

-0.763

(0.024) ***

-0.744

(0.030) ***

-0.760

(0.025) ***

8 -0.596

(0.039)***

-0.626

(0.039) ***

-0.328

(0.006) ***

-0.350

(0.034) ***

-0.365

(0.045) ***

-0.305

(0.036) ***

-0.258

(0.039) ***

-0.257

(0.039) ***

9 -0.715

(0.041)***

-0.727

(0.045) ***

-0.735

(0.037) ***

-0.577

(0.024) ***

-0.768

(0.050) ***

-0.759

(0.047) ***

-0.773

(0.054) ***

-0.760

(0.052) ***

10 -0.750

(0.040)***

-0.700

(0.051) ***

-0.751

(0.041) ***

-0.734

(0.044) ***

-0.711

(0.048) ***

-0.747

(0.041) ***

-0.740

(0.043) ***

-0.708

(0.049) ***

11 -0.239

(0.009)***

-0.196

(0.011) ***

-0.319

(0.009) ***

-0.340

(0.011) ***

-0.285

(0.009) ***

-0.269

(0.010) ***

-0.217

(0.011) ***

-0.214

(0.011) ***

b. Non-separable model (imperfect labor market)

1 -0.451

(0.012)***

-0.581

(0.013) ***

-0.561

(0.014) ***

-0.642

(0.042) ***

-0.528

(0.014) ***

-0.838

(0.011) ***

-0.569

(0.034) ***

-0.653

(0.040) ***

2 -0.431

(0.011)***

-0.684

(0.010) ***

-0.549

(0.014) ***

-0.516

(0.119) ***

-0.573

(0.013)***

-0.859

(0.008) ***

-0.423

(0.030) ***

-0.582

(0.039) ***

3 -0.669

(0.006)***

-0.671

(0.006) ***

-0.697

(0.013) ***

-0.784

(0.147) ***

-0.699

(0.006) ***

-0.680

(0.005) ***

-0.691

(0.020) ***

-0.703

(0.014) ***

4 -0.661

(0.007)***

-0.642

(0.010) ***

-0.660

(0.007) ***

-0.801

(0.129) ***

-0.684

(0.005) ***

-0.674

(0.005) ***

-0.694

(0.019) ***

-0.664

(0.025) ***

5 -0.326

(0.029)***

-0.413

(0.017) ***

-0.472

(0.015) ***

-0.427

(0.072) ***

-0.432

(0.037) ***

-0.482

(0.011) ***

-0.342

(0.066)**

-0.333

(0.053) ***

6 -0.763

(0.049)***

-0.773

(0.004) ***

-0.778

(0.005) ***

-1.260

(0.026) ***

-0.775

(0.005) ***

-0.782

(0.003) ***

-0.763

(0.012) ***

-0.783

(0.009) ***

7 -0.584

(0.009)***

-0.606

(0.008) ***

-0.576

(0.011) ***

-0.743

(0.030) ***

-0.553

(0.014) ***

-0.583

(0.008) ***

-0.615

(0.020) ***

-0.623

(0.022) ***

8 -0.763

(0.049)***

-0.625

(0.045) ***

-0.492

(0.039) ***

-0.350

(0.034) ***

-0.943

(0.055) ***

-0.549

(0.030) ***

-0.883

(0.180) ***

-0.603

(0.114) ***

9 -0.708

(0.006)***

-0.723

(0.007) ***

-0.787

(0.023) ***

-0.577

(0.024) ***

-0.798

(0.012) ***

-0.769

(0.007) ***

-0.873

(0.045) ***

-0.757

(0.011) ***

10 -0.681

(0.013)***

-0.637

(0.021) ***

-0.683

(0.015) ***

-0.734

(0.044) ***

-0.679

(0.017) ***

-0.652

(0.013) ***

-0.657

(0.040) ***

-0.660

(0.046) ***

11 -0.346

(0.048)***

-0.474

(0.055) ***

-0.451

(0.124) ***

-0.340

(0.011) ***

-0.598

(0.049) ***

-0.413

(0.039) ***

-0.329

(0.273) ***

-0.444

(0.109) ***

Note: i are conditional Hicksian own-price elasticities obtained from table A.1. Item indices: 1: Matooke; 2: Cassava;

3: Potatoes; 4: Maize; 5: Beans; 6: Meat and fish; 7: Fruits and vegetables; 8: Fats and oils; 9: Other foods; and 10:

Alcohol and tobacco; and 11: Leisure.( ***

) and (**

) denote significance level at 1 and 5%, respectively. A represents

non – agricultural households, B significant net sellers, C significant net buyers, D insignificant net sellers, and E

insignificant net buyers.


71

2.5.3 Welfare effects of price changes

The derivations of both shadow wages and different demand elasticities permit the computation of

welfare effects of food prices, using real changes between 2005/6 and 2009/10, and between

2009/10 and 2010/11. In computing these compensating variations, this essay diverges from almost

all the previous studies in two different ways. First, instead of applying hypothetical price

simulations as it is commonly done in many empirical studies on price shocks, the essay takes

advantage of the availability of household panel data collected during periods of stable and high

prices which allows to take account of changes that households really experienced. Second, and

contrarily to virtually all previous studies, we derive an expression of compensating variations

encompassing labor market frictions. We present in this paragraph successively first-order effects

and global (first- plus second-order) welfare effects of price changes under both perfect and

imperfect labor markets. We are thus able to evaluate the order of magnitude of these frictions. As

is standard in empirical literature, these compensating variations are expressed as the percentage of

the household real expenditures in the baseline periods (2005/06 for price changes between 2005/06

and 2009/10, and 2009/10 for changes between 2009/10 and 2010/11). These money-metric welfare

measures are reported such that positive (negative) values represent welfare losses (gains) due to

increases in real food prices. They indicate by what percentage an average Ugandan household

would have to increase (decrease) its current total expenditures to achieve the same utility level

attained in the corresponding comparison period.

First-order welfare effects of price changes

These first-order or direct effects only consider the immediate welfare consequences of price

changes without accounting for potential substitution mechanisms across commodities. What is

apparent from the results reported in table 2.11 is that the magnitude of these effects was dependent

of the poverty status of households47

, their net position in the food market, and the inclusion or not

of labor market frictions. Under separable models, real price increases between 2005/06 and

2009/10 led to an overall welfare gain of 11.1%, implying that a typical Ugandan household needed

to decrease its total expenditures by 11.1% in 2009/10 in order to reach the utility level achieved in

2005/06. However, this overall gain hides substantial differences among households. Non-

agricultural households are, unsurprisingly, among the biggest losers from price increases. Their

direct welfare losses were evaluated at 41.9%, suggesting that they would need to be compensated

47

Poverty lines were constructed using the Cost-of-basic-needs approach and applying the procedure proposed by Ravallion and Bidani (1993), and Appleton (2001).

Essay II

72

by about 42% of their food expenditures in 2009/10 in order to offset the effects of food price

increases between 2005/6 and 2009/10.

Table 2.11 Direct welfare effects of price changes between 2005/6 and 2010/11 under separability (SM) and

non-separability (NSM) (CV as a % of initial household expenditures)

Model

2005/6-2009/10 2009/10-2010/11

Coefficients Standard errors Coefficients Standard errors

All households

SM -0.111 0.026***

0.094 0.004***

NSM 0.136 0.058**

0.041 0.004***

Agricultural

SM -0.271 0.030***

0.079 0.005***

NSM 0.038 0.069 0.014 0.004***

Non-agricultural S/NSM 0.419 0.016***

0.155 0.008***

Rural

SM -0.270 0.031***

0.081 0.005***

NSM 0.078 0.034* 0.024 0.005

***

Urban

SM 0.489 0.034***

0.141 0.007***

NSM 0.355 0.085***

0.102 0.008***

Poor

SM 0.338 0.051***

0.115 0.004***

NSM 0.197 0.101*

0.044 0.004***

Non-poor

SM -0.208 0.031***

-0.090 0.011***

NSM 0.119 0.063*

0.031 0.012*

Significant net sellers

SM -0.269 0.053***

-0.149 0.007***

NSM -0.087 0.023***

-0.058 0.011

Significant net buyers

SM 0.211 0.032***

0.164 0.004***

NSM 0.078 0.012***

0.041 0.005***

Insignificant net sellers

SM -0.103 0.142***

-0.050 0.014***

NSM -0.045 0.022*

-0.019 0.008***

Insignificant net buyers

SM 0.061 0.011***

0.139 0.013

NSM 0.041

0.083 0.016

0.005***

Note: Standard errors are reported into brackets. (***

), (**

), and (*) denote significant levels at 1, 5, and 10%,

respectively.

Indeed, contrarily to agricultural households, these households cannot rely on agricultural revenues

to compensate for price increases. Furthermore, consistent with previous studies, poor and urban

households also experienced welfare losses of the order of 33.8 and 48.9% (Porto, 2010; Alem,

2011; Tefera et al., 2012). Notwithstanding agricultural households’ gains from price increases

(27.1% on average), welfare effects were unevenly distributed among them. Both significant and


73

insignificant net buyers suffered the most with respectively 21.1 and 6.1% of welfare losses. By

contrast, significant net sellers obtained the highest positive welfare effects (26.9% on average)

while, in comparison, insignificant net sellers benefited only marginally from price increases

(10.3%). As shown in table 2.4, significant net sellers experienced the highest increases in both crop

sales (+23.6%) and farm profits (+33.1%) between 2005/6 and 2009/10, which thereby increased

their profit effect and offset the magnitude of price fluctuations. While food prices also increased

between 2009/10 and 2010/11, Ugandan households globally lost from price upsurges. On average,

they had to increase their expenditures of 2010/11 by 9.4% if they wanted to remain at their

2009/10’s welfare level. The reason behind this contrasting picture could reside in the relatively

small price increases between 2009/10 and 2010/11 (21.4%) compared to increases in real prices

between 2005/6 and 2009/10 (139.2%). Only significant net sellers (14.9%) and to a marginal

extent, insignificant net sellers (5%) gained from price increases.

When we allow for imperfections in the labor market, the extent of welfare effects for all

households is strikingly reduced. Particularly during the first sub-period, Ugandan households as a

whole lost from price increases (13.6%). Although net sellers are still benefiting from food price

increases, their welfare gains decline in the first sub-period by 67.7% and 56.3% for significant and

insignificant net sellers, respectively, whereas the losses of net buyers are 63.3 % and 32.8% lower

for significant and insignificant net buyers, respectively. In the second sub-period, the global

welfare loss is now 56.4% lower than that obtained under no labor market frictions. These results

are in line with standard non-separable agricultural household models whereby market failures often

hamper farmers’ responsiveness to price changes or reduce their abilities to respond to price

incentives (Singh et al., 1986; de Janvry et al, 1991; Taylor and Adelman, 2003; Löfgren and

Robinson, 2002).

Welfare effects of price changes accounting for substitution effects

Although conclusions drawn from the first-order welfare effects provide useful primary insights of

price impacts, they have the drawback of ignoring the potential substitution effects of households

who generally substitute away from commodities whose relative prices have increased. Thus, they

tend to overestimate the negative impacts for welfare losers (non-agricultural households, poor, or

net buyers) and underestimate the positive effects for welfare gainers (agricultural and rural

households, net sellers). Accordingly, we also report in table 2.12 welfare effects accounting for

substitution effects.

Essay II

74

Table 2.12 Total welfare effects of price changes between 2005/6 and 2010/11 under separability (SM) and

non-separability (NSM) (CV as a % of initial household expenditures)

Model 2005/6-2009/10 2009/10-2010/11

Coefficients Standard errors Coefficients Standard errors

All households

SM -0.154 0.027***

0.042 0.004***

NSM 0.097 0.057*

0.019 0.003***

Agricultural

SM -0.299 0.031***

0.029 0.005***

NSM -0.009 0.068 -0.001 0.003

Non-agricultural S/NSM 0.238 0.017***

0.101 0.008***

Rural

SM -0.397 0.032***

0.031 0.005***

NSM 0.028 0.069 0.007 0.004*

Urban

SM 0.393 0.036***

0.082 0.008***

NSM 0.305 0.077***

0.060 0.006***

Poor

SM 0.265 0.052***

0.082 0.011***

NSM 0.100 0.055*

0.022 0.003***

Non-poor

SM -0.280 0.031***

-0.123 0.005***

NSM 0.085 0.019***

0.006 0.010

Significant net sellers

SM -0.354 0.053***

-0.200 0.007***

NSM -0.131 0.023***

-0.068 0.011***

Significant net buyers

SM 0.123 0.032***

0.113 0.005***

NSM 0.051 0.007***

0.024 0.002***

Insignificant net sellers

SM -0.177 0.143***

-0.101 0.013***

NSM -0.073 0.036**

-0.035 0.009***

Insignificant net buyers

SM 0.035 0.003***

0.086 0.013***

NSM 0.009 0.012 0.014 0.004***

Note: Standard errors are reported into brackets. (***

), (**

), and (*) denote significant levels at 1, 5, and 10%,

respectively.

Between 2005/6 and 2009/10, welfare gains increased on average by 38.7% under separability and

welfare losses decreased by 28.6% under non-separability. During the second comparison period,

welfare losses declined respectively by 53.7% and 55.3% in models with and without labor market

frictions respectively. The fact that these substitution effects are relatively high reflect large

possibilities of diet diversification in Uganda where none of the staple foods represents more than

20% of average daily caloric intakes (FAO, 2009a; Benson et al., 2008; Haggblade and Dewina,

2012). Households have therefore a bunch of possibilities to substitute away from expensive


75

commodities. However, not all households have the same improvements in their welfare estimates

when allowing for commodity substitution effects. For instance, between 2005/06 and 2009/10,

poor households recorded the smallest changes in terms of welfare effects. Their losses only fell by

21.6% against for example an increase of 34.6% for non-poor households under perfect labor

markets. Indeed, it is reasonable to think that since the diet of poor households is often made up of

cheap commodities, most possibilities of substitution have already been accounted for, hampering

the magnitude of their second-order effects. Furthermore, although agricultural households have

now gained from price increases in the non-separable models, these welfare effects were too small

(-0.9% and -0.1% in both sub-periods, respectively) to be significant. Between 2005/6 and 2009/10,

all agricultural households reported large changes in welfare effects due to substitution across

commodities under both separability and non-separability. However, during the second sub-period,

although second-order effects certainly dampened the extent of adverse welfare impacts of price

changes, they were insufficient to countervail them and transform first-order losers to overall

gainers.

The estimated welfare effects reported in tables 2.11 and 2.12 indicate the importance of accounting

for both labor market frictions and the net seller/buyer status of Ugandan households. These results

may also suggest that the estimated compensating variations could vary across the income or

expenditure distribution within the same sub-group of households. In order to explore this

possibility, we estimated non-parametric locally weighted regressions (LOWESS) using Gaussian

kernels. The first-order and total (first- and second-order) welfare effects are regressed on the

logarithm of real monthly total expenditures per adult equivalent for non-agricultural households

and all sub-groups of agricultural households. Figure 2.1 plots these various welfare effects’

distributions of price changes. The solid curves represent first-order effects while the dotted curves

display the welfare effects accounting for substitution across commodities. The horizontal dotted

line (at 0) gives the threshold below (above) which the welfare effects become positive (negative).

Keeping in mind that negative (positive) values of the compensating variations represent welfare

gains (losses), the general shape of the regression function (part 1.a.) seems to indicate that middle-

class households suffered the least from food price increases between 2005/6 and 2009/10. By

contrast, households located at the extremes of the expenditure distributions (the poorest and the

wealthiest households) were the most hit by price changes. While it is easier for rich households to

smooth their consumption without jeopardizing their food security or asset holdings, the poorest

households do not have large possibilities and may cope with price increases by reducing their

livestock or cuting off other household expenditures, such as education or health. On the other hand,

Essay II

76

a closer look at the different sub-groups helps grasp the differences in welfare distributions across

households. Among all sub-groups, non-agricultural households displayed the largest substitution

effects while the possibilities of substitution appear small for richer significant net sellers. However,

these second-order effects (the differences between the two curves) appeared particularly neutrally

distributed for non-agricultural households. At each percentile of expenditure distributions,

substitution effects are relatively of equal weight, contrarily for instance to significant

(insignificant) net sellers where households at highest (lowest) percentiles have much (less)

possibilities of substitution.

Figure 2.1 Non-parametric estimates of the relationship between compensating variations and household

expenditures (2005/6-2009/10) – Separable models


77

Dynamics of net market position and welfare effects

As shown in the previous paragraphs, the total welfare impact of price changes will hinge

essentially upon the magnitude of these changes, the extent of the market surplus or deficit, and

households’ sensitivity to price movements. In the case of a marginal deficit, the high consumption

cost due to increased food prices may be more than offset by higher income from agricultural

activities. This perspective may enhance the possibility to expand production and lead to a shift

from subsistence production to cash crop activities (Von Braun and Kennedy, 1994; Govereh et al.,

1999; Barrett and Dorosh, 1996) or even a change in the net market position of agricultural

households (Porto, 2010; Aksoy et al., 2010). For instance, using Mexican data, Porto (2010)

showed that farmers may change their net selling or buying status in case of large substitution

effects between crops grown and produced. Aksoy et al. (2010) also noted that between 1993 and

1998, price changes pushed about 21% of Vietnamese households to switch between being net rice

seller and net buyer. Among them, 15% net rice buyers in 1993 became net sellers by 1998, while

29% followed the inverse pathway.

Theoretically, in periods of large price increases, switching from a net buying to net selling position

would also change the welfare status from loser to gainer. A natural way to address these net

market position dynamics is by using transition matrices that depict a household net food position at

time t-1 and its current position at t. Table 2.13 summarizes these dynamics by showing the percent

of Ugandan households that shifted from one net market position to another during the first and

second sub-periods. The percents in the main diagonals (values in bold) give the proportions of non-

movers between t-1 and t while off-diagonal percents refer to household switchers.

A feature that immediately jumped out of these figures is the prominence of important dynamics.

First, in both sub-periods, non-agricultural households and significant net buyers appear trapped in

their respective sub-groups, especially in the second-period where around 89% and 77% of non-

agricultural households and significant net buyers did not change their net market position. Second,

it is revealing that some Ugandan households shifted from non-agricultural households to farmers.

This is particularly evident between 2005/6 and 2009/10 where 31.4% of non-agricultural

households become farmers, either net sellers (4.3%) or net buyers (27.2%). This proportion

dropped to 11% in the second period. A possible reason could be the relative attractiveness of

agricultural activities consecutive to food price increases during the sample period. Third, only less

than 50% of significant net sellers managed to maintain their status in both sub-periods and around

40% of them even became significant net buyers. Some of them forewent farming activities in

2009/10 (1.1%) and 2010/11 (3.9%). Fourth, in both sub-periods, insignificant net sellers and

Essay II

78

buyers were the most dynamic. Indeed, 41% and 34% of insignificant net sellers and net buyers in

2005/6 switched to being significant net sellers in 2009/10, whereas in 2010/1, these proportions are

reduced to 26% and 30%, respectively. However, the percent of agricultural households that shifted

from their initial status to becoming significant net buyers is the most important for all types of

farmers. Hence, by and large, it was relatively easier during the sample period for agricultural

households to switch to a significant net buyer status than shifting to any other type of household.

Table 2.13 Dynamics of food net market position between 2005/6 and 2010/11

2009/10

A B C D E Total

A 68.56 3.55 25.53 0.71 1.65 423

2005/6

B 1.09 48.01 39.49 5.80 5.62 552

C 6.42 1.66 62.33 3.04 4.08 1,152

D 3.70 40.74 45.68 6.17 3.70 81

E 2.64 34.31 55.88 1.96 4.90 102

Total 16.28 24.37 51.99 3.33 4.03 2,310

2010/11

2009/10

A B C D E Total

A 89.10 1.33 9.31 0.27 0 376

B 3.91 44.23 40.85 6.39 4.62 563

C 6.33 12.66 77.10 2.00 1.92 1,201

D 1.30 25.97 61.04 2.60 9.09 77

E 3.23 30.11 59.14 4.30 3.23 93

Total 18.92 19.65 55.97 2.90 2.55 2,310

Note: A represents non – agricultural households, B significant net sellers, C significant net buyers, D

insignificant net sellers, and E insignificant net buyers. The last columns give the total number of observations.

To see how these movements into and out of net seller/net buyer status translated into changes in

households’ welfare, we report in table 2.14 the average compensating variations of switchers and

non-movers from both separable and non-separable models. It is therefore possible to judge of the

“rationality” of each switch relative to the status quo. As expected, all households that became

significant net sellers gained from food price increases. However, in the first-sub period, the welfare

gains of switchers are much less important than those reported by non-mover significant net sellers,

whereas in the second period, the magnitudes of their welfare effects only slightly diverge.

Furthermore, in the first sub-period, agricultural households that abandoned their farming activities

lost more than non-agricultural households that did not switch.


79

Table 2.14 Net market position switching movements and welfare effects of price changes

2009/10

A B C D E

A 0.229 [0.229] -0.325 [-0.177] 0.082 [0.037] -0.114 [-0.09] 0.052 [0.034]

2005/6

B 0.256 [0.256] -0.577 [-0.196] 0.225 [0.075] -0.223 [-0.084] 0.042 [0.000]

C 0.267 [0.267] -0.299 [-0.184] 0.226 [0.049] -0.136 [-0.177] 0.027 [0.017]

D 0.287 [0.287] -0.367 [-0.329] 0.061 [0.024] -0.209 [-0.068] 0.033 [0.012]

E 0.254 [0.254] -0.365 [-0.042] 0.257 [0.014] -0.310 [0.014] 0.045 [0.031]

2010/11

2009/10

A B C D E

A 0.097 [0.097] -0.184 [-0.057] 0.175 [0.077] 0.017 [-0.008] -

B 0.161 [0.161] -0.192 [-0.062] 0.092 [0.019] -0.087 [-0.018] 0.071 [0.011]

C 0.104 [0.104] -0.217 [-0.086] 0.119 [0.025] -0.128 [-0.053] 0.101 [0.020]

D -0.004 [-0.004] -0.222 [-0.063] 0.102 [0.010] -0.148 [-0.006] 0.087 [0.000]

E 0.052 [0.052] -0.161 [-0.031] 0.083 [0.013] -0.079 [-0.103] 0.035 [0.092]

Note: A represents non – agricultural households, B significant net sellers, C significant net buyers, D

insignificant net sellers, and E insignificant net buyers. In each cell, total welfare effects (first-order plus second-

order effects) are reported. Compensating variations from non-separable models are displayed into brackets. (-):

no observation.

Overall, these figures suggest that it was “rational” during the sample period, at least in the

perspective of compensating variations, for non-agricultural households to engage into farming

activities, and particularly to become significant net sellers. For these latter, it was not in their

interest to change their status or if this happens anyway, they should stay net sellers, though

marginally. Significant net buyers would gain by shifting to a significant-net-seller position or if

this is impossible, they could minimize their welfare losses by reducing their food market deficit at

the levels of insignificant net buyers. Finally, insignificant net sellers would improve their positive

welfare effects of price changes by increase their market surplus, whereas insignificant net buyers

would rather be net sellers or, as in the second sub-period, drop from farming activities if they

cannot sustain their position.

2.6 Conclusions

The motivation behind this second study stemmed from the evidence of soaring food prices that

Uganda has been experiencing since 2008 and the lack of updated empirical studies on the potential

consequences of price changes on households. To that end, the study made use of a non-recursive

Essay II

80

agricultural household model under the assumption of labor market imperfections to derive the

welfare effects of price surges between 2005/6 and 2010/11. The data came from three of the latest

waves of the Uganda National Panel Surveys (UNPS) collected in 2005/6, 2009/10, and 2010/11

and covering each 2,310 households from all the four geographical regions of the country and

periods of both stable and volatile food prices.

On the production side, the separability hypothesis has been rejected, suggesting that household’s

production and consumption decisions were intertwined. On the consumption side, the QUAIDS

model specification has been tested and adopted to derive expenditure and price demand elasticities

of ten commodities groups, namely matooke, cassava, potatoes, maize, beans, meat and fish, fruits

and vegetables, fats and oils, other foods, alcohol and tobacco, as well as leisure time. To allow for

household’s heterogeneous behavior with regards to food price changes, households were divided

into five exclusive groups based on their net market position: non-agricultural households,

significant net sellers, significant net buyers, insignificant or marginal net sellers and insignificant

net buyers.

It appeared that Ugandan households not only reacted differently to price changes but also were

differently affected by food price inflation between 2005/6 and 2010/11. Results from the

compensating variations revealed that welfare effects of price changes were on average globally

lower when labor market imperfections are accounted for, which implies that separable models tend

to overstate welfare impacts of price shocks. Further, locally weighted scatterplot smoother

(LOWESS) regressions showed that, globally, for most household categories, welfare losses were

the highest for the poorest and, surprisingly, richest categories. This provides evidence that not only

welfare effects of price changes were unequally distributed both within the same household group

and between different household categories, but also that poor households were those who suffered

the most from price upsurges, exacerbating the vulnerability to other types of shocks. Finally, the

estimation results shed light on important dynamics that occur in the net food market position for

most households. In particular, we found that a significant proportion of agricultural households

switched from a net seller to net buyer position and the other way around. As consequence, the

welfare effects of price changes also reported a similar pattern during the sample period.

Although the above conclusions help understand what happened to Ugandan households between

2005/6 and 2010/11, two important facts should be kept in mind. First, our findings are ultimately

anchored to the assumption of a partial equilibrium framework, particularly that all other sources of

changes are being held constant. We therefore left out the potential spillover or multiplier effects

that food price increases might have induced to the rest of the Ugandan economy (Akson and


81

Hoekman, 2010). For example, between 2005 and 2011, the Ugandan economy grew annually at an

average rate of 7.7% (WDI, 2012), and this could have dampened the negative effects of price

shocks through income increases. Allowing for these spillover effects through a general equilibrium

model might improve our estimates (de Janvry and Sadoulet, 2006). Second, we estimated direct

welfare impacts and allowed for substitution effects across commodities by using only

compensating variations and ignoring the risky nature of household activities, most of whom being

agricultural. Hence, it is possible to extend the analysis carried in the present study by estimating

for example the extent to which Ugandan households would be willing to pay for price stabilization

(Bellemare et al., 2013) or by incorporating risk factors both in the consumption and production

sides of households.

82

Essay III

How strongly do agricultural risks and farmers’ expectations

influence acreage decisions?

Dynamic models of land use in Uganda

3.1 Introduction

Farming is inherently a risky activity. Between the planting and harvest seasons, agro-climatic and

economic conditions wherein the farmers operate can change drastically. The consequences of

production decisions, generally made well in advance, are thus imperfectly predictable, leading to

farm revenues either better or worse than expected (Harwood et al., 1999; Hardaker et al., 2004).

There are different types of risks to which a farmer is regularly exposed, among which

production/yield and price risks. Production risk originates from supply shocks often related to

weather conditions, such as insufficient or excessive rainfall and precipitation, extreme temperature,

or from pest infestations. On the other hand, price risks are usually related to fluctuations caused by

changes in both demand and supply conditions (Coyle, 1992, 1999; Just and Pope, 2001; Isik,

2002).

Different management tools may help the farmers protect themselves ex-ante against production

and price uncertainties48

or mitigate ex post their adverse consequences. These strategies range from

crop insurance, production or futures options contracts, hedging in futures, to enterprise

diversification (Harwood et al., 1999). While many of these options may mitigate the extent of

production and price risks, their applicability in developing countries is quite limited due to various

institutional and structural constraints, such as poor or absence of well-organized formal insurance

and credit markets, the apparent complexity of such coping mechanisms for most farmers, often

under-educated, or simply the lack of confidence and interest in those management tools. As an

alternative, most farmers in developing countries rely on self-insurance measures to cope with

agricultural risks and market fluctuations. They often make different adjustments in the cropping

48

The terms risk and uncertain are used interchangeably in the study

Essay III

83

pattern across both crops and agricultural seasons when they anticipate important changes in

weather or market conditions.

Understanding and evaluating the impact of both yield and/or price expectations and their

variability on crop choices and acreage allocations have thus become the focus of attention of many

applied agricultural economics’ studies. These studies, some dating back many decades, have

developed both theoretical and empirical models of farmers’ responses in presence of price and

yield uncertainties. In one of the early attempts to study acreage decisions under multivariate risk,

Chavas and Holt (1990) estimated a system of acreage equations for corn and soybean in the United

States and found that both risk and wealth variables were significant determinants of corn-soybean

acreage allocation decisions. Also, Fafchamps (1992) showed that, in developing countries, crop

diversification is generally preferred by small farmers as a response to high price variance in the

absence of formal insurance mechanisms. Recently, the swing in commodity prices in 2008, to

levels not seen since the early 1970s, led to abundant empirical studies questioning the adjustement

of land uses to these price changes (Hausman et al., 2012, and Livingston et al., 2008, 2014 for the

United States; Weersink et al., 2010 for Ontario in Canada; Lacroix and Thomas, 2011 for France).

In Sub-Saharan Africa, several studies have been conducted on the determinants of land allocations.

Among them, Chibwana et al. (2011) and Mponela et al. (2011) reported that household

characteristics (age, education, sex, land ownership, and non-farm incomes) were the main drivers

of changes in land distribution patterns in Malawi. Constructing farmers’ risk indices from

Ethiopian data, Bezabih et al. (2011) found that crop portfolio choice was essentially influenced by

rainfall variability and that farmers were likely to choose less risky crops at the expense of high

returns. In Uganda, Mwaura (2014) concluded that access to infrastructure, households’ stock of

education and cultivated area were the key factors that affect land allocations.

Methodologically, different approaches have been applied to estimate acreage response functions.

They range from the estimation of structural models of multi-output profit function, input

allocations and land use (Carpentier and Letort, 2009; Fezzi and Bateman, 2011; Lacroix and

Thomas, 2011; Kaminski et al., 2013) to reduced-form crop choice models (Bezabih et al., 2011;

Anderson and Wang, 2012; Allen, 2012).

Built on these studies, this third essay aims at modeling and estimating the responsiveness of

agricultural land allocations to changes in agro-climatic and economic conditions, with a particular

emphasis on price and yield risks and farmers’ expectations of their levels. The study revisits

acreage response models based on the theoretical framework of Chavas and Holt (1990), Coyle

(1992), and Holt (1999) in order to investigate the main drivers of crop portfolio decisions by


84

farmers in developing countries under risks and unobserved farm and crop heterogeneity. It makes

several contributions to the existing empirical studies on farmer’s acreage responses.

First, it explores two intertwined dimensions related to acreage decisions that are often emphasized

in the literature, namely a multivariate crop selection and the allocation of land area to each

potential crop. To take account of this interdependence, farmers’ acreage responses are modeled as

a two-step procedure. During the first step, farmers determine which crop(s) to grow given their

expectations of end-of-season prices and yields, their volatility, and other control variables (weather

volatility, farmer and land characteristics…). Conditional on the selected crops, farmers then decide

how to share out their land.

Second, while the majority of the previous studies are essentially based on static models and

therefore ignore the dynamic nature embodied in agricultural activities, this essay models farmers’

decisions as a dynamic process, thereby capturing the possibility of both own and cross state

dependencies as well as distinguishing between genuine and spurious state dependencies.

Third, most of the existing studies have centered their attention on aggregated or county-level

estimations of land use allocations. Although aggregated data are generally easily accessible and

substantially minimize the presence of corner solutions, they present the downside of ignoring farm

heterogeneity within counties or regions (Fezzi and Bateman, 2011). In this study, farmers’ acreage

decisions are modeled and estimated using farm- and plot-level data. These data are often very

comprehensive and provide complete information on input uses at plot level, land use allocations,

farmers’ revenues, costs, and capital likely to improve the empirical analysis of farmers’ crop

decisions. Furthermore, the panel nature of the data allows to control for unobserved farm

heterogeneity which is often a major component in land-use models (Wu et al., 2004; Lacroix and

Thomas, 2011).

Fourth, although farm-level data permit direct estimations of acreage share responses to exogenous

shocks, the presence of important amount of zero observations in land-use allocations and the

bounded nature of the land shares complicate the econometric analysis. To deal with these issues,

most studies estimate crop share models using essentially multivariate Tobit specifications. The

main drawback of these specifications is that they wrongly treat zero observations as a result of

censoring and cannot ensure that the predicted crop shares will lie between 0 and 1 or sum up to 1

for each farmer. As an alternative specification which assures that the above conditions are met, this

study uses a multivariate generalization of the fractional regression model49

proposed by Papke and

49

In her study of land allocations in Uganda, Mwaura (2014) also used a fractional multinomial logit model. However, the model presented here fundamentally differs from hers in many aspects. First, she only made use of 2 survey rounds (2005/6 and 2009/10) while the present study takes advantage of the last four household surveys in Uganda and therefore generalizes her results and provides much more robust estimates and interpretation. Second, her

Essay III

85

Wooldridge (1996, 2008) and recently applied by Sivakumar and Bhat (2002), Mullahy and Robert

(2010), Lopez-Garcia and Montero (2010), Wagner (2010), Koch (2010 ), and Mullahy (2011). The

estimation approach is applied to six crops or crop groups (matooke, cassava, maize, potatoes,

beans, and other cereals) using a four-wave balanced panel of 1,598 agricultural households in

Uganda using data collected between 2005 and 2012 by the Uganda Bureau of Statistics (UBoS) as

part of the Living Standards Measurement Study-Integrated Surveys on Agriculture (LSMS-ISA) of

the World Bank.

The results indicate that incorporating past farmers’ crop choices and accounting for unobserved

heterogeneity significantly improve the predictability performance of the land use models, thereby

highlighting the importance of modeling crop choice decisions as a dynamic process. They also

shed light on the presence of both strong inertia (positive own state dependence) for all crops but

moderate spillover effects (significant cross-state dependence) for most crops. Moreover, farmers

are found to be more sensitive to changes in expected yield levels than in expected end-of-season

output prices, and yield risks, temperature and rainfall volatility have more impact on crop choices

and acreage share allocations than market price risks.

The remainder of the essay proceeds as follows. Section 3.2 presents the conceptual model and its

theoretical predictions. Section 3.3 discusses both the empirical implementation of the theoretical

model and the related econometric issues. Section 3.4 describes the data used in the estimation of

crop choice and acreage share models and further details the construction of some key variables and

presents their descriptive statistics. Section 3.5 presents and discusses the main econometric results.

Section 3.6 evaluates the prediction performance of the models and finally, section 3.7 gives some

concluding remarks.

3.2 Theoretical model

In this section, I outline the theoretical model and the main assumptions made. Some of them are

justified by the specificities of the Ugandan agricultural economy and the focus of the present study

on price and yield risks, and land allocation constraints, while others mainly respond to the

necessity to render the empirical models as tractable as possible and to minimize data requirements

(Bonfatti, 2010). To motivate the econometric analysis, I develop a conceptual model in which a

representative farmer has land as the only fixed allocation input. That is crops compete for

model is essentially static and does not take account of unobserved heterogeneity among farmers or crops. Last but not least, her analyses leave aside the influence of risks (production, price, and weather risks) in driving farmers’ acreage decisions.


86

allocations of a fixed amount of land, and consequently increases in the land share of one crop in

the short run implies inevitably the adjustments in the land allocations of other crops.

Consider a farmer that grows K different crops subject to the total land available L . Furthermore, let

y be a 1K vector of end-of-season yields (per acre) for the K crops, with elements ky ; p a 1K

vector of end-of-season output prices, with elements kp ; w a 1K vector of per-acre production

costs, with elements kw ; a a 1K vector of acreages allocated to the K crops, with elements ka ;

and as *)/1( L a 1K vector of acreage shares for the K crops, with elements ks . While

production costs are generally known during the planting season, end-of-season outputs and crop

prices are unobserved by the farmer at the time the production decisions are made because of

various factors generally beyond the farmer’s control (rainfall variability, loss of all or part of

production due to pest infestations,…) and must therefore be based on farmers’ expectations.

Following Coyle (1999), I adopt a mean-variance approach which expressed the utility to be

maximized U in terms of the first two moments of the farmer’s profit (expected profit E

and profit risk 2 ). The objective of the farmer is to maximize the expected utility of profit given

the fixed land allocable constraint. Under both price and yield risks, the problem can be stated as:

1thatsuch

,cov2var2

1

1

1

22

1

K

k

k

K

kj

kjkj

K

k

kk

K

k

kk

s

rrssrsLrEsLMax s

where E is an expectation operator; kkkk wypr is the per-acre net return of crop k.

kkkek

ek

ekk wypyprrE ,cov is the per-acre expected net return of crop k, with e

kp and eky the

expected price and per-acre yield of crop k; ks is the acreage share devoted to crop k; is the

Arrow-Pratt coefficient of absolute risk aversion which indicates risk-averse, risk-neutral, and risk-

seeking attitude if 0and,0,0 , respectively50

. Equation (3.1) sheds light on the

role of both risks (price and output) and farmer’s risk attitude on the acreage allocation process.

From equation (3.1), the K + 1 first-order conditions to the farmer’s optimization problem are given

by:

KkrrsrsLLrs

LK

kj

kjjkkek

k

,...,1,0,cov)var(2

50

Throughout this essay, farmers are assumed to present some degree of risk aversion, as consistently outlined in many empirical studies (Binswanger, 1980 and 1981; Chavas and Holt, 1990; Pope and Just, 1991).

(3.1)

(3.2)

Essay III

87

01

1

K

k

ksL

The solution to these FOCs gives a system of K optimal acreage share equations ,,,,* Lrwps

and the optimal value of the Lagrange multiplier associated with the land constraint ,,,,* Lrwp

, with r , the variance-covariance matrix of crop returns.

To see how these optimal acreage shares are modified by changes in price or yield risks, let us

assume that the farmer only grows two competing crops, j and k51

and that 1 . Under the above

model assumptions, the FOCs can be expressed as follows:

1011

1)var(),cov(

1),cov()var(

22

22

Lr

Lr

s

s

rLrrL

rrLrL

ek

ej

k

j

kjk

kjj

The system of optimal acreage shares and Lagrange multiplier associated with this model is then

given by:

22222222

2

2

*

*

*

)var(

1

jkjkkjkejjjk

ek

jkjej

ek

jkkek

ej

kjk

j

LLrLr

Lrr

Lrr

rrLs

s

where jkkjkj rr 2var 22 ; )var(2kk r ; )var(2

jj r ; ),cov( kjjk rr

Equation (3.5) reflects implicitly the patterns of both crop substitution and complementarity as it

asserts that the optimal acreage share allocated to the first crop will depend on the differential in

expected net returns, the total land available and the price and yield risks of each crop (through the

variance and covariance of their net returns).

How will the farmer react to a change in each of these variables? For simplicity, consider the case

of statistical independence between end-of-season price and yield. In this case, the variance and

covariance of the net returns are:

222222)var(var kekk

ekkkkkk ypypr

and

jkek

ej

ek

ejjkjkkkjjkj yyppypypErr ),(,cov

where )var(2kk p ; )var(2

kk y ; ),cov( kjjk pp ; ),cov( kjjk yy

The sensitivity of the acreage shares to changes in price and yield risks ( 2j , 2

j ) and expected

output prices ( ejp , e

kp ) can then be summarized as follows:

51

The analysis can be readily generalized in case of K (>2) competing crops. See Holt (1999).

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)


88

Drsrs

D

NppLDppLyps

NifD

NppLDLpyps

NifD

NpLs

NifD

NyLs

ejk

ekj

jkejk

ek

ejjkk

ek

eke

kj

jkjk

ekj

ej

ekjk

eje

jj

ejjjj

ejjjj

/1//

22ˆ/

0and002

/

00/

00/

**

2

22*

2

2*

2

222*

2

222*

with )var( kj rrLD and jkkek

ej LrrN 2

In equations (3.8a) – (3.8d), optimal acreage share responses of crop j to changes in various

exogenous variables are essentially driven by the differential in the expected net returns of the

crops, ek

ej rr , the net return variance of the competing crop k, and the covariance between the net

returns of j and k. For example, under the model assumptions, relation (3.8a) states that a risk-

averse farmer will reduce the acreage allocated to a crop j in response to increases in its price

variance only if its expected net return exceeds that of crop k ( ek

ej rr ) and the expected net returns

of k and j are either uncorrelated or negatively correlated ( 0jk ) . With regards to crop prices,

equations (3.8c) and (3.8d) indicate that the responses of acreage shares to changes in expected

prices are not straightforward. Hence, if the farmer anticipates a positive shock to the expected

own-price of crop j, then the theoretical model predicts that he will allocate more land to that crop

only if both yield and net return covariances are zero or negative, and that ek

ej rr . When it comes to

the changes in the price of the competing crop, the model fails to predict an unambiguous sign even

if one assumes that the expected prices, yields, and net revenues change in opposite directions. The

sign will ultimately depend on the relative importance of each component.

Finally, by using the symmetry condition in (3.8e), the relation between price elasticities of acreage

shares of j and k is given by:

ykj

yjk

pjk

ek

ej

pkj

/

where ** // k

e

j

e

jk

p

kj spdpds and ** // jek

ekj

pjk

spdpds are land shares’ elasticities of k and j to

changes in expected prices of j and k; ** // jek

ekj

yjk

sydyds is the land share elasticity of j to

changes in expected yields of k; Lrs ejj

ej and Lrs e

kkek are expected profits of crops j and k.

From (3.9), the cross-price acreage share elasticities of crops j and k would be equal pjk

pkj

only

(3.8d)

(3.8e)

(3.8c)

(3.8b)

(3.8a)

(3.9)

Essay III

89

when both the crop-specific expected profits are equal ek

ej and yield elasticities of land shares

are equal ykj

yjk

.

3.3 Empirical specification

The empirical specification is guided by the two main objectives of this third essay: on the one

hand, understand how farmers decide which crops to grow given agricultural and market-related

risks, farmers’ expectations, and household characteristics; and on the other, what proportion of

land should be optimally allocated to the selected crops. It follows that a farmer’s acreage decisions

can be modeled as a two-step decision process. Firstly, the participation or selection step during

which the farmer chooses the crops to grow. Secondly, the conditional acreage allocation step

wherein the farmer derives the optimal acreage share for each selected crop. As pointed out by

Lacroix and Thomas (2011: 785), this is a case of multivariate crop selection problem since “(…)

unobserved components may affect the choice of several crops by the farmer while influencing the

final outcome in terms of land for crop (…)”. Each above model allows farmers’ land decisions to

be determined by both current farm, farmer (un)observed characteristics and past land use

decisions, leading to a dynamic crop allocation model. The estimation of these dynamic models

seeks to verify a possible state dependence in farm acreage decisions and support for adjustment

effects in farmers’ land use, i.e. on the one hand, if farmers tend to continue to grow a crop once

they have grown it previously or instead support for crop rotational effects; and on the other, if

farmers maintain the same land share profile over time.

Referring to the notation used in the previous section, let *hktI and *

hkts denote respectively the latent

response variable and latent acreage share corresponding to the kth crop in the hth farm at time t, for

,,...,1;,...,1 NhKk and Tt ,...,1 ; let also hkt

I and hkts represent their observable counterparts.

The latent dependent variables in the selection and acreage share models associated with each crop

k at time t can be expressed as follows:

tkhs

tkhI

hkthkt

hkthkt

,,,'

,,,'*

*

k2

k1

γV

βV

where 1V and 2V are vectors of independent variables, sharing some common elements. In 1V is

also included a vector of lagged dependent variables 1, thkI , for Kk ,...,1 , taking 1 if the farmer h

grows crop k at time t – 1 and 0 otherwise. 2V also contains the vector of lagged acreage shares

(3.10)

(3.11)


90

1, thks , for Kk ,...,1 , which allows current farmers’ decisions about a particular crop k to be

influenced by previous allocation decisions on all competing crops.

and are time-invariant unobserved heterogeneity which may exist at both the household level

(for example unobserved farmer’s ability) and the crop level (for example, suitability of a particular

crop to specific types of land). hkt and hkt are error terms, assumed identically and independently

distributed.

The dynamic structure in both (3.10) and (3.11) creates two theoretical and methodological

problems: the initial conditions’ problem and the treatment of unobserved heterogeneity. The well-

known initial conditions’ problem stems from the fact that the start of our observational period may

not necessarily coincide with the start of the stochastic process underlying farmers’ choices

(Heckman, 1981a, b; Wooldridge, 2005a). In other words, crop and acreage decisions at time t = 1

(our first observational time period) depend on farmers’ data at time t = 0, unavailable to the

econometrician. As suggested by Wooldridge (2005a), one way of preventing estimators from being

biased and inconsistent under the initial conditions’ problem is to include as an additional regressor

the value of the dependent variable at time t = 1 (initial crop choice or initial acreage share,

depending on the model). The second problem is related to the treatment of unobserved

heterogeneity. A within-transformation procedure cannot be applied to get rid of or due to the

nonlinearity of the models. Also, introducing 1K dummy variables to estimate the unobserved

heterogeneity will result in biased estimation of parameters in (3.10) and (3.11), unless T , the

so-called incidental parameters problem (Wooldridge, 2005a). Following Papke and Wooldridge

(2008) and Lacroix and Thomas (2011), I thus apply the Mundlak-Chamberlain approach which

consists in writing and as a linear function of individual averaged values of time-varying

covariates52

. A similar approach has been applied by Erdem and Sun (2001), Devicienti and Poggi

(2007), and Buddelmeyer and Wooden (2008). Taking account of both the initial conditions’ and

incidental parameters’ problems, the unobserved individual heterogeneity in each crop equation k is

expressed as follows:

Kkahkkk ,...,1,' 2hkk1h1 υυ'Δ

Kkwith ,...,1,,,,, ,2,1 hkhkhkh1h1h1 V,VsIΔ

52

The Mundlak-Chamberlain approach relies on the assumption that and are normally distributed. Although this

seems restrictive, it is easier to implement. To allow for a more flexible functional form, a non-parametric strategy, similar to that of Heckman and Singer (1984) could be adopted. However, the flexibility it allows comes at cost, like the non-convergence of the estimator or the impossibility to inverse the Hessian to get standard errors (Bigsten et al., 2006).

(3.12)

Essay III

91

where are individual random effects, assumed to be K-variate normal with variances 2

k and

covariance between k and j given by jkjk . h1I and h1s are the vector of first observations of

farm choice and acreage shares in farm h, respectively;

T

tT 1

1hkthk ;

hk2,hk1,hk V,V . hka

is a random component assumed distributed 2,0 aktN .

These models are estimated for six main crops or crop groups: matooke ( 1k ), cassava ( 2k ),

maize ( 3k ), potatoes53

( 4k ), beans ( 5k ), other cereals54

( 6k ), and a residual category

defined as “other”55

( 7k ). In what follows, I describe more in detail the estimating equations for

the selection and acreage share models and the econometric issues they raise.

3.3.1 Dynamic multivariate selection model

In this model, farmers are not restricted to choosing only one crop among the K possible

alternatives56

. Indeed, farmers in developing countries are often poorly insured against agricultural

and market-related risks (price and yield variability, weather shocks…). To cope with such risks,

they generally engage in crop diversification (Fafchamps, 1992; Kurosaki and Fafchamps, 2001;

Mukherjee, 2010) by adopting a multi-cropping system with the hope that crops with relatively

stable prices will compensate revenue variability caused by crops with more volatile prices.

Furthermore, due to potential complementarity or substitutability between the crops to grow, it is

most likely that the error terms in each crop selection model will be correlated with one another,

advocating therefore for a simultaneous estimation of farmers’ crop selection decisions. To allow

for a possible multi-cropping strategy among farmers and the presence of both unobserved

heterogeneity and state dependency, I estimate the multivariate selection model using a dynamic

multivariate probit (Dynamic-MVP) regression:

tkhIII hktk

K

jhjjk

K

jthjjkkhkt ,,,''

11

11,

*

2hk υZβZ

with

TtKkNhII hkthkt ,...,1;,...,1;,...,1,01 *

53

Irish and sweet potatoes 54

Rice, millet, and sorghum 55

Crops and/or land uses included in this « other » category are farm-specific. They include crops such as groundnuts, wheat, or soybeans. 56

It is theoretically possible to ensure that alternatives will be mutually exclusive even when the farmer can choose

more than one crop (Train, 2003). However, when K is large, there is 12 K possible crop combinations (excluding

the one where no crop is grown) which represents 63 alternatives in a 6-crop choice model, as in this study (See Appendix C.1).

(3.13)


92

The error terms hkt jointly follow a K-variate normal distribution with zero conditional mean and

variance of 1, and a symmetric KK covariance matrixΣ . In this dynamic setting, true state

dependence effects are captured through the dummies of the lagged dependent variables. The model

also helps test for the presence of dynamic spillover effects in farmers’ decisions by including

cross-lagged values.

Let MhktΩ denote the vector of all right-hand side (RHS) variables in the dynamic multivariate crop

selection model and Mθ be the vector of all parameters to be estimated. To derive marginal

probabilities, let MMjjj cw θΩ ' and 12 jj Ic , for Kk ,...,1 , where the subscripts h and t

have been suppressed for convenience. In this case, the probability of observing a particular crop

choice j among all possible combinations is given by (Cappellari and Jenkins, 2003):

MM MMK

MMj

KjjKjK

jKjKKjKj

ddd

wwwwwwIII

θΩ θΩθΩ' '

11

'

111

1......;,...,,...,......

;,...,,...,,...,,...,0,...,1,...,0Pr

where .K and .K are K-variate normal density and probability distribution functions,

respectively. jjj RR with jR is a K x K diagonal matrix with diagonal elements jc et zeros

elsewhere. In this K-variate probit model, it is straightforward to show that the log-likelihood

function is (Greene, 2003):

N

h

K

k

T

t

jKjKtkh wwwIL

1

1

1 1

1,, ;,...,,...,lnln

The estimation of this dynamic-MVP model was done using the Simulated Maximum Likelihood

(SML) method with the Geweke-Hajivassiliou-Keane (GHK) simulator. The dynamic-MVP

regression framework has previously been applied in various studies, including Seo and

Mendelsohn (2007) for a multi-country analysis of African farmers’ livestock choice under climate

change scenarios, Oparinde and Hodge (2011) for households’ adoption of coping strategies against

health shocks in rural Nigeria, or Fleming (2014) for the adoption of management practices among

Maryland farmers.

3.3.2 Dynamic acreage share model

An important aspect in farming activities consists usually in deciding how much of the available

land to allocate to different crops. As discussed early, this decision can be affected by both current

and past allocation decisions. Otherwise stated, I seek to evaluate the expected value of *

hkts , given

(3.14)

(3.15)

Essay III

93

the covariate vector hktX , unobserved farm- and crop-specific effects , and past acreage shares

1, thks , .,...,1 Kk

To deal with potential sample selection in a multivariate setting, I apply a generalization of the

Heckman two-step method proposed by Tauchmann (2005, 2010). The main virtue of this approach

is that rather than restricting the estimation procedure to the subsample of farmers with positive

crop selection as is commonly done, each element of the RHS is weighted by hktI so that the

estimation is based on the full sample and conditioned on hktI .57

Therefore, the second-step

estimation of (3.11) is based on the conditional expectation:

khkkkhkthkt ζ'ZγZ'βX'X kkhkthkhkthkthkthkhkt IIIIsE ,, , tkh ,,

In each equation k, the inverse Mills ratio khkk ζ'ZγZ' k from the first-step multivariate crop

selection model is included as an additional covariate with k , its parameter to be estimated.

Given equation (3.11) and the procedure in (3.16), the dynamic crop acreage model has the

following form:

0

1

0

'' ,1 1

111,,0

hkt

hkthktkk

K

j

K

jhjjthjjkkk

hktI

I

if

ifsss

k2hk υXγX, thk ,,

In (3.17), the coefficients Kkjk ,..,1, capture own- and cross-true state dependence effects.

Hence, the acreage share of crop k at time t hkts is assumed to depend on both its previous acreage

share ( 1, thks ) and acreage shares allocated to alternative crops 1, thjs , kj . This enables to test for

the present of dynamic spillover effects in farmers’ crop decisions.

In estimating equation (3.17), we need to take account of the fact that the dependent variables

(acreage crop shares) and their predicted values have two-corner outcomes, 0 and 1, with non-trivial

probabilities and continuous values between 0 and 1. This relates to fractional dependent variables

(Papke and Wooldridge, 1996, 2008) and implies that 0, thks if 0* hkts ; *,, thkthk

ss if 10 * hkts ;

and 1, thks if 1* hkts .

There is a long tradition in econometrics of estimating share or fractional models. Their applications

include modeling time use, optimal portfolio shares, consumer budgets, or land use allocations.

Various estimation strategies have been proposed in the literature to account for the bounded nature

57

See Tauchmann (2005, Appendix A) for details. The estimation of the second step on the subsample of farmers for

which 1hktI would lead to severerly unbalanced panel. Hence, this approach is particularly useful in the present

study since the Woodridge’s method of handling the initial observations’ problem requires a balanced panel.

(3.17)

(3.16)


94

of the dependent variables. Early econometric attempts were applied in demand analysis for the

estimation of systems of food consumption under censoring (Christensen et al., 1975; Deaton and

Muellbauer, 1980; Banks et al., 1997; Yen et al., 2003). Recently, Fezzi and Bateman (2011) and

Lacroix and Thomas (2011) estimate land use shares using a system of two-limit Tobit models via

quasi-maximum likelihood. Despite the widespread use of uni- or multivariate Tobit models on

fractional data among researchers, the estimated results do not guarantee that the fitted values will

lie between 0 and 158

. In their seminal paper, Papke and Wooldridge (1996) develop a robust

Quasi-Maximum Likelihood (QML) model, as in Gouriéroux, Monfort and Trognon (1984) for the

estimation of a univariate fractional regression model through a Bernoulli log-likelihood function.

Papke and Wooldridge (2008) extend their previous model to panel data and develop a QML

estimation method to account for endogeneity. Several generalizations of Papke and Wooldridge

works to the multivariate setting have been recently proposed to model various issues, from

commodity flows (Sivakumar and Bhat, 2002) to transportation time (Ye and Pendyala, 2005),

expenditure shares (Koch, 2010), household time use (Mullahy and Robert, 2010), financial asset

portfolio (Mullahy, 2011), corporate capital structure choices (Ramalho, Ramalho, and Murteira,

2013) and education tests (Nam, 2012).

Along the lines of Mullahy and Robert (2010), and Mullahy (2011), I use a dynamic multivariate

fractional logit (dynamic-MVFL) model to estimate equation (3.17). Indeed, one way of ensuring

that the conditional mean 1,0

S

Ωhkt

sE and that 1

1

K

k

Shkt

sE Ω is to use a multinomial logit

functional form:

KkQ

KlQsE

K

l

Sl

S

Sk

SSk

Sk

K

l

Sl

S

Sk

SSk

SSk

Shkt

,

'exp1

'exp'

,...,1,

'exp

'exp';

1

1

1

θΩ

θΩθΩ

θΩ

θΩθΩθΩ

where SΩ denote the vector of all RHS variables in the dynamic-MVFL model and S

kθ the vector

of all parameters to be estimated in the kth equation. Similarly to standard multinomial logit

models, identification of the multivariate fractional logit requires the normalization of one of the

parameters. In this essay, I chose the share of “other crops” (k = 7) (equation (3.18b), implying that

07 SS

K .

58

Another reason of the inappropriateness of the use of Tobit models is simply because the dependent variables are not actually censored since values outside the 0-1 interval are not feasible (Baum, 2008).

(3.18a)

(3.18b)

Essay III

95

Assuming that the functional form in (3.18a) is correct and given the identification assumption in

(3.18b), the multivariate fractional likelihood log-function is given by:

SSk

N

h

K

k

T

t

tkh QsL θΩ 'lnln

1

1

1 1

,,

The estimated parameters are then obtained from the first order conditions applied to (3.19)59

. As is

well known in any two-step estimation procedure, second-stage standard errors of parameter

estimates will be incorrect because they are derived from the first-stage participation model. In the

empirical estimation, I rely on bootstrapping methods60

. However, the normalization required by the

adding-up restriction renders difficult the interpretation of point estimates derived from the

maximization of (3.19). To obtain results that are invariant with the type of normalization selected,

the estimates of interest are acreage elasticities computed at sample average, and defined as the

relative effect of a covariate jx on the expected conditional means hktXtkhsE ,, . For continuous and

discrete exogenous variables, these effects are given respectively by equations (3.20a) and (3.20b)

(Mullahy and Robert, 2010):

jkjhtKkjjkjhtK

N

i

T

t

ijt

N

i

T

t

K

l

lljkjijttkh

j

j

tkhjk

XQXQxNT

QxNTsE

x

x

sE

,,,,

1 1

1 1

1

1,,

,,,

ˆˆˆ1

ˆˆ1

ˆ

ˆˆ

hkt

hkt

X

X

where jk , stands for the estimated expected acreage elasticity of crop k with respect to changes in

the covariate jx . Due to the adding-up restriction,

K

j jk1 , 0 , which implies that the effect of a

covariate will lead to a reallocation of land across crop alternatives. is the estimated parameter;

tkhs ,,ˆ is the estimated share of land allocated to crop k by household h in year t. jhtX , is the

covariate vector for the h-th observation, excluded the j-th element.

To investigate the causal factors of both multivariate crop choices and crop acreage shares, I include

in hktX and hktZ six categories of explanatory variables, namely expected output prices ( e

ktp ) and

59

The estimation of the multivariate fractional logit model was done using a Quasi-maximum likelihood function programmed in Stata’s Mata language written by John Mullahy who kindly provided the author with the codes. Although his approach was primarily intended for cross-sectional data, it can be readily extended to the panel data case by appealing to the Correlated Random Effects approach to estimation (Chamberlain, 1980 and Mundlak, 1978) and specifying the conditional mean of the unobserved effect as a parametric function of the time-averages of the independent variables as in (3.12). 60

The number of replications used was chosen following the approach proposed by Andrews and Buchinsky (2000). Each crop share was estimated separately to derive the optimal number of bootstrap replications which were then averaged out in the multivariate fractional logit estimation.

(3.19)

(3.20a)

(3.20b)


96

yields ( e

kty ), their respective risk measures ( e

ktvp and e

ktvy ), farm or land characteristics, climatic

variables, and farmer’s characteristics. Referring to land characteristics, I control for total land size

( tld ), land quality ( ldq ), type of land irrigation ( tdir ), and the nature of land slope ( ldsp ). ldq

measures the proportion of fertile plots (land of good quality) in the total plots cultivated by the

farmer; ldir , the proportion of rain-fed plots, and ldsp , the proportion of plots with flat or gentile

slopes. Climatic variables include the average expected monthly rainfall ( mar ), its coefficient of

variation ( marcv ), the temperature deviation ( dmt )61

and its coefficient of variation ( dmtcv ).

Farmer’s characteristics contain the years of education ( educ ), age ( age ), and gender ( sex ) of the

household head, as well as the household size ( hsz ). I impose exclusion restrictions by including in

hktZ adult ratio ( adr )62

, non-farm income ( nfi ), and regional dummies variables.

3.4 Data and construction of variables

The implementation of the acreage allocation model described in the previous section requires a

substantial amount of data regarding crop choices, farmers’ expectations of output prices and yields,

farm and farmer characteristics, and climatic variables. Data on crop choices, land use and size,

variable input prices and quantities (labor, seeds, pesticides, fertilizer,…), farm and household

characteristics are obtained from a four-wave panel dataset of the Uganda National Panel Surveys

(UNPS) conducted in 2005/6, 2009/10, 2010/11, and 2011/201263

by the Uganda Bureau of

Statistics (UBoS). For this study, each wave contains information on 1,598 balanced agricultural

households, located in all the geographical regions of the country. Pooling these time series and

cross-sectional data gives 6,392 observations for the crop choice and acreage allocation models

(1,598 farmers x 4 years).

3.4.1 Plot size

The surveys report two measures of land size: GPS measures and farmer’s own estimation.

However, while area measures from farmers’ own assessments are available for almost all plots,

GPS-based area measures suffer from important missing values due to various constraints such as

61

The difference between monthly maximum and minimum temperatures (in degrees Celsius). 62

Defined as the ratio between the number of household members above 18 and the total household size 63

The first wave (2005/6) collected agricultural information for the second cropping season of 2004 (July-December 2004) and first cropping season of 2005 (January-June 2005). The remaining waves gathered information for the two cropping seasons (January-June and July-December) of 2009, 2010, and 2011, respectively. Hence, to avoid confusion from the reader between the timing of the surveys and the periods they actually covered for the agricultural module, I will subsequently refer to the panels in terms of waves 1 to 4.

Essay III

97

“[…] reducing survey costs, […] keeping household interview durations within reasonable limits,

and […] the difficulty of asking respondents to accompany enumerators to agricultural plots that are

situated far from dwelling locations […]” (Kilic at al., 2013: 3). To deal with these missing GPS-

based data, I apply a multiple imputation approach initiated by Rubin (1987).64

Hence, in all the

subsequent analyses, land size will refer to multiply imputed land areas.

The persistent or transitory nature of distributional land patterns can be analyzed using transition

matrices for successive panel waves65

. Results presented in table 3.1 indicate unequal land

dynamics during the sample period.

Table 3.1 Bivariate transition matrices of changes in the distribution of total land holdings

Land size in 2011/12 (acres)

]0 ; .6[ [.6 ; 1.25[ [1.25 ; 2.5[ [2.5 ; 7[ [7 ; 10[ >=10 N. obs.

Land size in

2005/6

(acres)

]0 ; .6[ 46 23.9 17.2 10 1.4 1.5 402

[.6 ; 1.25[ 19.2 26.1 25.8 25.3 1.5 2.1 395

[1.25 ; 2.5[ 8.1 15.7 29.4 36.5 6.1 4.2 394

[2.5 ; 7[ 6 7.3 19.3 49.1 8.5 9.8 316

[7 ; 10[ 2.9 5.7 0 57.1 17.1 17.2 35

>=10 3.8 8.9 12.5 26.8 7.1 41.1 56

Land size in 2009/10

]0 ; .6[ [.6 ; 1.25[ [1.25 ; 2.5[ [2.5 ; 7[ [7 ; 10[ >=10 N. obs.

Land size in

2005/6

]0 ; .6[ 60.2 22.4 10.2 5.7 0 1.8 402

[.6 ; 1.25[ 24.1 40.8 22.8 9.9 1.5 .9 395

[1.25 ; 2.5[ 8.9 28.4 36.3 21.3 2 3.1 394

[2.5 ; 7[ 7.6 11.4 22.2 44.9 5.1 8.8 316

[7 ; 10[ 2.9 14.3 8.6 45.7 11.4 17.1 35

>=10 5.4 8.9 8.9 25 8.9 42.9 56


]0 ; .6[ [.6 ; 1.25[ [1.25 ; 2.5[ [2.5 ; 7[ [7 ; 10[ >=10 N. obs.

Land size in

2009/10

]0 ; .6[ 55.3 25 11.8 5.8 .8 1.5 400

[.6 ; 1.25[ 16.6 32 29.6 17.6 .7 3.5 409

[1.25 ; 2.5[ 5.1 19.6 35.5 32.7 3.4 3.7 352

[2.5 ; 7[ 3.5 5.3 18.2 54.1 7.9 11 318

[7 ; 10[ 2.6 2.6 5.1 33.3 25.6 30.8 39

>=10 8.8 1.3 7.5 22.5 8.8 51.3 80


]0 ; .6[ [.6 ; 1.25[ [1.25 ; 2.5[ [2.5 ; 7[ [7 ; 10[ >=10 N. obs.

Land size in

2010/11

]0 ; .6[ 54.6 19.9 13.8 8.9 1.2 1.6 326

[.6 ; 1.25[ 23.2 40.4 23.5 10.7 1.6 .6 319

[1.25 ; 2.5[ 10.9 15.3 39 31.5 1.9 1.4 359

[2.5 ; 7[ 3.9 8.7 17.4 58.1 7.3 4.6 413

[7 ; 10[ 1.7 3.3 15 36.7 26.7 16.7 60

>=10 5.8 5 11.6 29.8 8.3 39.7 121

Note: Each cell gives the row percentage.

64

The Stata’s mi impute command has been used to impute these missing values. (See Appendices C.2 – C.4). 65

The intervals were constructed from the pooled distribution of land sizes. Farms were divided into 2 broad categories: small farms (<10 acres) and large farms (>=10 acres). Small farms were then subdivided into 4 groups using respectively the 25th percentile, the median, the mean, and the 75th percentile as bounds. For each survey, extreme or outlier values were defined as those beyond the 99

th percentile and replaced by values observed at that percentile.


98

Between the first and last wave (part one of the table), important transitions are observed but state

persistence is relatively mitigated: for example, only 46% of farms with less than 0.6 acres

remained in the same state in the last wave and 1.5% increased their land size up to more than 10

acres. However, between successive waves, the table uncovers very high persistence, particularly

for states 1 and 4. For example, although there is a significant decrease over time in the persistence

rate within state 1 (from 60.2 to 55.3 and 54.6%), persistence in state 4 shows instead a significant

increase (from 44.9 to 54.1 and 58.1%), suggesting that likelihood of moving from state 1 (very

small farms) to other states (medium or large farm sizes) increased over time.

3.4.2 Representation of price expectations and risks

At the time production decisions are made, a farmer ignores what will be the end-of-season output

prices. The empirical implementation of crop choice and acreage share models thus requires a

statement on how farmers form their expectations about future prices and their related risks. There

is no consensus as to how variables representing riskiness in prices should be formulated in

econometric models. Various models of price expectations tested for agricultural commodities

include: naive expectations (Houck and Gallagher, 1976; Shumway and Chang, 1980; Chavas and

Holt, 1990), adaptive expectations (Nerlove, 1958), rational expectations (Muth, 1961; Goodwin

and Sheffrin, 1983; Shonkwiler and Emerson, 1982; Beach et al., 1995, among others), futures

prices (Schroeder and Goodwin, 1991), or a combination of the previous models (Lopez, 1986;

Tada, 1990). The naive expectations model states that today’s price is simply the most recently

observed (or previous) price; the adaptive expectations model argues that the expected price is the

weighted average of the previous price and the previous expected price, with geometrically

declining weights; the rational expectations model assumes that expectations are formed based on

the relevant structure of the economic system given all relevant information available to the farmers

when planting decisions are made. Finally, the composite expectations model considers the

expected price as a weighted average of prices based on adaptive and rational expectations.

These expected prices were computed using monthly real food prices66

from time series’ prices

collected by the Foodnet market price information project of the International Institute of Tropical

Agriculture (IITA). The Foodnet dataset consists of weekly wholesale price series for 23 Ugandan

66

For each series, nominal prices were deflated by the UBoS all items’ consumer price index (2005/06=100) to take account of potential changes in the purchasing power of Ugandan households.

Essay III

99

markets67

and more than 20 staple foods from September 1999, week 40 to December 2012, week

5268

.

Let tMp , be the market price of crop i at time t ande

tNp , ,e

tAp , ,e

tRp , , and e

tMXp , denote its expected

value derived from the naive, adaptive, rational, and composite expectations models, respectively.

Following Chavas et al. (1983), Chavas and Holt (1990), and Tada (1990), etNp , and e

tAp , can be

written as:

1,, tMe

tN pp

jtMjt

n

J

j

jntMne

tAtMe

tAe

tA pEppppp

,1

1 1

,1

1,1,1,, ω1

where 1 jtE is the expectation, when crop i is planted at time t – j , of the end-of-season price in

year t – j and .1,1 jtMjtjt ppE jω are declining weights as we go back in time and are

expressed as 1

12ω

JJ

jJj , with J the number of lags (Hommes, 1998). For simplicity, I only

consider the case where J = 3 (i.e the past three observed market prices)69

. Given etNp , and e

tAp , , the

expected price variances are defined as a weighted sum of the squared deviations of the past 3

market prices from their respective expected values. Formally, the expected price variance of crop

k, 2kt , and expected price covariance of crops j and k in time t, jkt , are expressed as follows:

23

1

1,,,2 ω

i

eitkitkikt pp

eitA

eitN

eit

eitkitk

eitjitj

i

ijkt ppppppp 1,1,1,1,,,1,,,

3

1

,with,ω

In regards to the rationally expected pricese

tRp , , I draw on the work of Feige and Pearce (1976) and

Nerlove et al (1979) who have shown that rational expectations can fundamentally be approximated

using ARIMA specifications. I test the order of integration of each price series allowing for the

67

Arua, Gulu, Kitgum and Lira in the Northern region; Luwero, Masaka, Rakai, Kiboga, and Kampala (Kisenyi, Owino, Nakawa, Kalerwe) in the Central region; Iganga, Mbale, Jinja, Soroti, and Tororo in the Eastern region; and Jinja, Kabale, Kibale, Kasese, Hoima, and Mbarara in the Western region 68

The use of market-level data to derive price expectations of economic agents is not exempt from criticisms. Overall, the main criticism is the assumption of homogenous information set for all market participants (Pesaran, 1987). Therefore, in the absence of data on farmer-level expectations over output prices, the analysis carried out in this third essay should be considered as an indirect approach of deriving price formation in Uganda. 69

In this case, the weights are given by 5.ω1 , 33.ω2 , and 17.ω3

(3.21a)

(3.21b)

(3.22a)

(3.22b)


100

possibility of structural breaks using Bai and Perron (2003) tests70

. Appendix C.5 reports the

ARIMA estimates for the selected price series71

. The same procedure is applied to derive expected

price variances of each price series.

Knowinge

tRp , , the composite expected price is given by etR

etA

etMX ppp ,,, 1 , where

10 72

. Crop price risks ( eiMX

eiR

eiA

eiN vpvpvpvp ,,,, ,,, ) are thus defined as the square root of the

expected price variances derived from different expectations models.

To identify which expectations model best describes the price formation process, I use a simple

unbiasedness test from the estimation of the following relationship:

te

ttM pp ,, * , with etMX

etR

etA

etN

et ppppp ,,,,, ,,,

In order for price forecasts to be consistent with observed prices, they should be unbiased predictors

of the actual market prices. This implies that the intercept 0 and the slope 1 at 5%

significant level (Beach et al., 1995). Appendix A.6 contains the results of the unbiasedness tests.

They suggest that the null hypothesis of unbiasedness is rejected for all commodities in the naive

(except for other cereals), adaptive, and rational (except for maize) expectations models. However,

when we combine the adaptive and rational expectations models using the values that offer the

best statistical fits (Adjusted R – squared)73

for the price expectation model (3.23), we fail to reject

the null hypothesis of unbiasedness for all selected commodities. In other words, at the market

level, the estimated results advocate for a mixed expectations model rather than a pure naive,

adaptive, or ARIMA models. Consequently, all expected prices and price risks used in the crop

choice and acreage share estimations will refer to the composite expectations model. Lopez (1986),

Tada (1991), and Chembezi (1994) have also demonstrated the high capacity of the composite

models in explaining price expectations behavior.

3.4.3 Expected yields and yield risks

To obtain the expected yields ( e

ky ), we need to identify the set of weather variables likely to

influence the level of end-of-season yields. It is well-established for example that the levels of

70

In the case of structural breaks or shifting trends in price series, the standard Augmented Dickey-Fuller (1981), Phillips-Perron (1988) unit root tests become biased because of their potential confusion of structural breaks in the series as evidence of non-stationarity (Ghoshray, Kejriwal, and Wohar (2012). See essay I, section 1.4.1. 71

Results of the unit root tests (not presented here) indicated that all price series were I (1). Hence, in the

qdp ,,ARIMA estimation results, the price series were first-differenced (d = 1). 72

In the extreme case where 0 , producers are assumed to form their expectations based solely on the ARIMA

specification. On the opposite side 1 implies price expectations according to the adaptive model. Finall, when

10 , both adaptive and rational models are accounted for in farmers’ price expectations. 73

0.3 for cassava and beans; 0.4 for matooke and potatoes; 0.5 for maize and 0.6 for other cereals.

(3.23)

Essay III

101

rainfall, precipitation, and temperature are important factors in determining crop yields (Mitchell et

al., 1990; Porter and Semenov, 2005; Lobell et al., 2007). To derive farmers’ expected yields, I

follow the specification proposed by Chavas and Holt (1990) and applied in numerous empirical

studies (see, for example, Lin and Dismukes, 2007; Weersink, et al., 2010; Liang et al., 2011):

hkdtkddtdthkdt ty 'W

where hkdty is the current yield of crop k for a farmer h living in cluster/district d at time t. W is a

vector of weather variables74

in district d at time t (expected monthly rainfall mar and deviation in

temperature dmt and their coefficients of variation marcv and dmtcv ) and their quadratic terms to

allow for non-linear effects of weather factors (Porter and Semenov, 2005); kd is district-level fixed

effect, and t denotes a linear time trend. Equation (3.24) was then estimated separately for each crop

k.

Given that data on yields are left-censored at 0, I used a panel Tobit regression and take out the

predicted values as expected yields. Crop yield risk ( e

ktvy ) was then measured as the standard

deviation of the estimated residuals from the Tobit model.

Appendix C.7 defines key variables and presents their descriptive statistics.

3.5 Empirical results

3.5.1 Dynamic multivariate crop selection model

The estimated coefficients of the dynamic multivariate crop selection model reported in table 3.2

are derived from the empirical specification elaborated in equation (3.13). The model was

estimated using the Simulated Maximum Likelihood (SML) method and the GHK simulator, with

initial conditions a la Wooldridge. As suggested by Cappellari and Jenkins (2003), I choose the

74

I obtain data on climatic characteristics from various annual issues of the Statistical Abstracts of the UBoS. These data contain monthly information on temperature (degree Celsius) and rainfall (mm). Although yield data are at farm level, data on temperature and rainfall were only available for 12 meteorological stations covering all the geographical regions of the country: Arua, Gulu, and Lira in the Northern region; Entebbe and Kampala in the Central region; Jinja, Soroti, and Tororo in the Eastern region; and Kabale, Kasese, and Mbarara in the Western region. These data were then merged with farm survey data for the respective years. Similarly to Coyle (1999), mean and variance of weather

variables in station s at time t were first computed as: 1, tsst and 2,,

3

1

ω)var( itsits

i

ist

, with the

weights iω being defined as in (3.22). For each region, these means and variances were then averaged over their

respective stations.

(3.24)


102

number of draws (100)75

greater than the square root of the sample size (80) to reduce the

simulation bias. I also derived starting values from univariate random-effects probit regressions

(Cappellari and Jenkins, 2006; Fezzi and Bateman, 2011) and dropped from the final model

variables that presented a high collinearity, particularly covariances between expected prices.

We first note that all coefficients of pairwise correlations between error terms ( ij ) are statistically

significant, supporting the hypothesis of interdependence of farmers’ crop choices and the

appropriateness of a joint estimation of the crop selection equations. Moreover, the likelihood ratio

test rejects at a high significance level the hypothesis that all pairwise correlations of error terms are

simultaneously zero. The model prediction also appears satisfactory since the marginal predicted

probabilities of success for each crop choice 1Pr kI are in all cases greater than 50%.

Globally, the signs of the explanatory variables are in line with our predictions and most variables

of interest are significant at least at 5% level. The coefficients of lagged dependent variables

highlight the existence of a great degree of true state dependence in crop choices. Put differently,

after controlling for observed and unobserved heterogeneity, past crop choices significantly and

positively influence current farmers’ decisions. This crop persistence over time may be explained

by both farmers’ preferences and specific constraints. For example, the costs of transitioning from

one crop to another may be sufficiently high due to differences in input requirements or agronomic

constraints that a farmer may simply decide to maintain this past land allocation pattern.

In addition, there is evidence of cross-persistence in farmers’ choices for most crops, as suggested

by the coefficients of lagged variables of alternative crops. Most of these coefficients are negative,

implying crop rotational effects. Indeed, it is well documented that growing the same crop year after

year on the same plot may result in low yields and high costs, while cultivating a sequence of

different crops over several planting seasons could ultimately increase land profitability (Choi and

Sohngen, 2003; Livingston et al., 2008). Alternatively, changes in profitability due to expected

changes in relative prices of different crops may convince a farmer to adjust his future land

allocations. Similarly to lagged variables, own initial observations significantly increase the chances

of growing crops, contrarily to most initial values of competing crops.

With respect to price expectations, all estimated coefficients of own-expected prices are not only

significant but also have the expected signs: farmers’ anticipations of an increase in expected

market prices positively affect the likelihood of selecting and growing crops. Conversely, the more

volatile the expected crop prices, the lower the likelihood of crop selection, as implied by the

negative and significant sign of all expected own price risks.

75

I also tried alternative numbers of draws (150, 200, and 500) but final results did not significantly improve.

Essay III

103

Table 3.2 Coefficient estimates-Dynamic Multivariate Probit model

Coefficient estimates

matooke cassava maize potatoes beans Ot. cereals

State dependence variables

1,1 tI 1.261 (0.073)*** -0.068 (0.069) -0.164 (0.065)** -0.033 (0.065) 0.203 (0.069)*** -0.154 (0.066)**

1,2 tI -0.017 (0.063) 0.755 (0.057)*** 0.045 (0.056) 0.157 (0.057)*** -0.051 (0.066) -0.239 (0.061)***

1,3 tI -0.025 (0.065) 0.066 (0.055) 0.499 (0.056)*** 0.021 (0..053) 0.050 (0.057) -0.006 (0.054)

1,4 tI -0.146 (0.057)** 0.108 (0.055)** -0.038 (0.055) 0.569 (0.052)*** -0.065 (0.054) -0.044 (0.052)

1,5 tI 0.266 (0.071)*** -0.107 (0.065)* 0.212 (0.061)*** -0.005 (0.058) 0.717 (0.061)*** -0.188 (0.061)***

1,6 tI -0.187 (0.064)*** -0.083 (0.038)** -0.112 (0.056)** -0.053 (0.056) -0.145 (0.059)** 0.813 (0.057)***

Initial observations

1,1I 0.372 (0.072)*** -0.119 (0.073)* 0.026 (0.073) 0.105 (0.064)* 0.206 (0.076)*** -0.113 (0.054)*

1,2I -0.060 (0.065) 0.527 (0.055)*** -0.024 (0.061) 0.037 (0.055) -0.037 (0.063) -0.018 (0.063)

1,3I 0.145 (0.073)** -0.047 (0.063) 0.398 (0.058)*** 0.008 (0.058) -0.045 (0.065) -0.096 (0.062)

1,4I 0.035 (0.064) 0.040 (0.056) 0.075 (0.057) 0.303 (0.051)*** -0.026 (0.059) 0.025 (0.059)

1,5I 0.266 (0.073)*** -0.002 (0.068) -0.171 (0.065)*** -0.071 (0.029)*** 0.460 (0.063)*** -0.099 (0.053)*

1,6I -0.133 (0.067)** -0.139 (0.060)** -0.078 (0.056) 0.022 (0.054) -0.197 (0.062)*** 0.561 (0.059)***

Expected output prices and price risks

ep1 0.413 (0.024)*** -0.066 (0.030)** -0.016 (0.030) -0.036 (0.029) -0.043 (0.039) -0.016 (0.029)

ep2 -0.008 (0.009) 0.328 (0.011)*** 0.016 (0.007)** 0.001 (0.007) 0.015 (0.011) 0.007 (0.008)

ep3 -0.002 (0.001)* -0.001 (0.002) 0.429 (0.004)*** 0.004 (0.003) -0.001 (0.002) 0.002 (0.000)***

ep4 -0.018 (0.018) 0.026 (0.023) 0.025 (0.019) 0.071 (0.035)* -0.066 (0.029)** -0.039 (0.021)*

ep5 -0.020 (0.001)*** 0.008 (0.019) -0.032 (0.022) -0.031 (0.023) 0.151 (0.030)*** -0.056 (0.021)***

ep6 -0.038 (0.037) 0.063 (0.035)* 0.028 (0.049) -0.024 (0.056) -0.129 (0.050)*** 0.202 (0.112)*

evp1 -0.355 (0.049)*** -0.001 (0.037) 0.077 (0.035)** -0.033 (0.033) 0.049 (0.045) 0.006 (0.035)

evp2 -0.048 (0.052) -0.469 (0.075)*** -0.106 (0.043)** -0.047 (0.043) 0.009 (0.051) -0.040 (0.043)

evp3 0.046 (0.055) -0.037 (0.048) -0.513 (0.131)*** 0.071 (0.035)* 0.021 (0.063) -0.041 (0.049)

evp4 -0.013 (0.060) -0.108 (0.057)* 0.012 (0.052) -0.571 (0.091)*** -0.015 (0.056) 0.054 (0.052)

evp5 0.093 (0.051)* 0.022 (0.045) 0.027 (0.044) -0.008 (0.040) -0.291 (0.066)*** -0.067 (0.038)*

evp6 0.004 (0.040) -0.021 (0.039) -0.051 (0.041) 0.013 (0.038) -0.014 (0.044) -0.083 (0.042)*

Expected yields and yield risks

ey1 1.005(0.173)*** -0.149 (0.105) 0.067 (0.011)*** 0.085 (0.109) -0.190 (0.112)* 0.098 (0.057)*

ey2 -0.160(0.068)** 0.613 (0.025)** -0.004 (0.024) 0.039 (0.031) -0.044 (0.025)* 0.083 (0.062)

ey3 0.107 (0.097) 0.015 (0.169) 0.624 (0.011)*** 0.109 (0.045)** -0.007 (0.009) 0.203 (0.108)*

ey4 0.063 (0.151) 0.152 (0.152) 0.138 (0.149) 0.259 (0.154)* - 0.056 (0.149) 0.229 (0.159)

ey5 -0.193 (0.208) -0.297 (0.213) -0.318 (0.211) -0.342 (0.212)* 0.475 (0.021)*** 0.099 (0.237)

ey6 0.109 (0.173) 0.088 (0.006)*** 0.278 (0.171)* 0.176 (0.196) 0.104 (0.198) 0.583 (0.240)**

evy1 -0.589(0.266)** -0.630(0.466) -0.557(0.462) -0.505(0.463) -0.630(0.464) -0.703(0.507)

evy2 -1.314(0.339)*** -1.210(0.330)*** -1.241(0.322)*** -1.289(0.330)*** -1.174(0.330)*** -0.956(0.437)**

evy3 -0.532(0.332)* -0.604(0.306)** -0.684(0.299)** -0.611(0.309)** -0.675(0.299)** -0.096(0.452)

evy4 0.478(0.721) 0.019(0.701) 0.109(0.699) -0.411(0.179)*** 0.189(0.703) -0.095(0.726)


104

Table 3.2 (continued)

matooke cassava maize potatoes beans Ot. cereals

evy5 0.547(0.688) 0.048(0.679) 0.009(0.684) 0.066(0.688) -0.470(0.027)** -0.159(0.698)

evy6 -0.486(0.296)* -0.440(0.266)* -0.484(0.273) -0.411(0.279) -0.495(0.282)* -0.323(0.150)**

Climatic variables

mar -0.073 (0.004)*** -0.014 (0.005)*** -0.010 (0.005)** -0.029 (0.004)*** -0.063 (0.005)*** -0.031 (0.006)***

marcv -1.230 (0.438)*** -1.386 (0.423)*** -0.446 (0.042)*** -0.629 (0.057)*** -1.036 (0.413)*** -0.417 (0.048)***

dmt -0.416 (0.102)*** -0.381 (0.102)*** -0.045 (0.011)*** -0.327 (0.094)*** -0.033 (0.104) -0.212 (0.092)**

dmtcv -1.530 (0.494)*** -1.897(0.805)** -0.308 (0.076)*** -1.758 (0.988)*** -0.101 (0.008)*** -0.431 (0.079)***

Land characteristics

tld 0.142 (0.040)*** 0.085 (0.033)** 0.120 (0.035)*** 0.081 (0.032)*** 0.179 (0.039)*** 0.147 (0.034)***

ldq 0.143 (0.017)*** 0.064 (0.015)*** 0.290 (0.140)** 0.060 (0.032)* 0.011 (0.006)*** 0.061 (0.006)***

ldir 0.013 (0.068) 0.041 (0.059) 0.031(0.053) 0.051 (0.131) 0.004 (0.147) 0.042 (0.163)

ldsp -0.225 (0.117)* -0.055 (0.093) 0.082 (0.092) -0.223 (0.092)** 0.031 (0.103) -0.191 (0.096)**

Household characteristics

educ 0.087 (0.001)*** 0.148 (0.076)** 0.082 (0.048)** 0.090 (0.039)** 0.034 (0.013)*** 0.023 (0.016)*

age 0.719 (0.278)** -0.031 (0.317) 0.281 (0.0259) -0.103 (0.284) -0.493 (0.317) 0.026 (0.304)

sex 0.112 (0.060)** 0.056 (0.054) 0.011 (0.053) -0.023 (0.049) -0.042 (0.058) 0.031 (0.056)

hsz 0.278 (0.112)** 0.162 (0.096)* 0.101 (0.012)*** 0.089 (0.048)** 0.123 (0.069)** 0.131 (0.002)***

adr 0.163 (0.153) -0.030 (0.131) -0.255 (0.131)* -0.124 (0.121) 0.020 (0.144) -0.354 (0.138)***

nfi 0.008 (0.005)* -0.000 (0.004) -0.011 (0.004)*** -0.003 (0.004) 0.001 (0.004) -0.004 (0.004)

Ctl 0.234 (0.092)*** -0.063 (0.784) 0.347 (0.693) -0.128 (0.707) 0.658 (0.418)** -0.619 (0.004)***

East -0.027 (0.339) 0.121 (0.083)*** 0.648 (0.282)*** 0.471 (0.133)*** 0.029 (0.352) -0.899 (0.067)***

W est 0.092 (0.033)*** 0.024 (0.002)*** 0.529 (0.312)* 0.208 (0.035)*** 0.886 (0.397)** 0.064 (0.007)***

Cons 3.791 (2.135)* 6.598 (1.937)*** 0.960 (2.083) 6.296 (2.101)*** 5.854 (2.369)** 5.453 (3.147)*

ij

j1 1 0.066 (0.038)* -0.048 (0.006)*** 0.042 (0.005)*** 0.087 (0.041)** -0.145 (0.038)***

j2 1 0.038 (0.002)*** 0.277 (0.029)*** 0.036 (0.016)** -0.106 (0.031)***

j3 1 0.107 (0.029)*** 0.297 (0.032)*** -0.025 (0.000)***

j4 1 0.152 (0.033)*** 0.041 (0.010)***

j5 1 -0.059 (0.034)*

j6 1

1Pr kI 0.692 0.713 0.720 0.591 0.721 0.609

Note: Robust standard errors into parentheses. ***, **, and * indicate statistical significance at the 1, 5, and 10%

levels, respectively. ij stands for the coefficient of the correlation between error term of crops i and j.

Likelihood of all 0000.0,021.587,2:,0 2

33 valuepjiij

This suggests that higher but more volatile expected prices of a specific crop may dissuade a farmer

from growing it in favor of more stable crops in terms of prices, implying a price risk-averse

attitude. Similarly to output prices, the estimated coefficients of expected yields are found to be

positive and significant while increases in own yield risks are detrimental to crop selection.

In terms of climatic variables, increases in expected monthly rainfall only have a very marginal

effect on crop selection while changes in its volatility (measured by changes in coefficient of

Essay III

105

variation) significantly and negatively affect current land decisions. Analogously, it is changes in

volatility of temperature spreads (difference between average monthly maximum and minimum

temperatures) rather than in their mean values that influence the most farmers’ crop choices. These

results are consistent with findings by Wu et al. (2004) and Weersinsk et al. (2010).

Land characteristics also diversely influence farmers’ crop selection decisions. Whereas increases

in the total agricultural land size and the proportion of good-quality plots positively increase

farmers’ crop participation, the proportion of both rain-fed and flatted plots appears irrelevant in

explaining farmers’ crop choices, probably because most agricultural plots (more than 90%) were

only rain-fed or had flatted/gentile slopes (around 85%).

In addition, most demographic variables do not significantly influence crop choices. Exceptions are

household size and the level of education of the head. Household size increases the likelihood of

growing all selected crops. This result is in accordance with the characteristics of the agricultural

sector in most developing countries where not only agriculture is primarily of subsistence but also a

large share of labor involves self-employment. In this context, increasing family size constrains the

household to either increase farm production (through more land areas to cultivate or improved

productivity) or seek off-farm labor opportunities. In all equations, the level of education attained

by the farmer appears to have a positive and significant impact on crop selection. Finally, the

estimated coefficients of most regional dummies variables are significant, suggesting important

cluster and geographical effects due probably to agro-climatic specificities76

.

3.5.2 Dynamic acreage share model

The second model is the selectivity-corrected dynamic acreage share model which specifies the

factors affecting land area allocations by Ugandan farmers. Appendix C.8 presents the estimation

results of the dynamic multivariate fractional logit models with (Model I) and without (Model II)

unobserved heterogeneity accounted for. I discarded from the final results covariates with high

collinearity, particularly covariances of expected prices and yields as well as some time-averaged

variables from the Mundlak-Chamberlain transformation.

Let us first take heed to the variables related to state dependence ( 1, thjs ) and initial conditions ( 1hjs

). At first glance, all crops exhibit significant own state dependence, whether I allow for individual

heterogeneity or not. The share of each crop in the current period hkts depends positively on the

acreage share previously allocated to that crop 1, thks . The results further show that the initial land

76

For example, matooke is generally consumed in western, central, and southern parts of the country. cassava is generally grown in northern, northwestern and eastern regions of Uganda.


106

allocation 1hks is an important determinant of current acreage decisions, which suggests, according

to the empirical framework, a significant correlation between farmers’ “pre-sample” and current

characteristics. The results also reveal the presence of significant dynamic spillover effects among

the acreage equations, implying a strong cross state dependence. These estimated effects are

negative and consequently the share of each crop in the current period is negatively influenced by

the shares of alternative crops in the previous period. Thus, for a fixed, allocatable land size in a

multicrop system, the acreage model reveals a competition among crops for area shares. It can also

be noted that the coefficients of lagged dependent variables are mostly larger (in absolute values) in

models II, where unobserved heterogeneity has been ignored, resulting in an overestimation of the

effects of state dependence. This feature is however expected because the effect of the uncontrolled

unobserved heterogeneity is partly included in the coefficients of lagged outcome terms (Divicienti

and Poggi, 2007).

To check whether the addition of lagged dependent variables improves acreage model performance,

I also estimated a static-MVFL (models without state dependency and initial observations problem).

The comparison of the estimated coefficients (presented in Appendices C.8 and C.9) indicates that

the magnitude of most coefficients tend to decrease (in absolute values) when we go from the static

to dynamic models. These differential impacts can be attributed to the fact that the variables in the

static models are absorbing parts of the effects otherwise captured by state dependency.

However, these parameter estimates are not per se informative of the marginal effects of the

covariates on the acreage shares. To analyze their partial effects, tables 3.3-3.5 show the expected

acreage elasticities using equations (3.20a) and (3.20b) for both the static and dynamic models with

unobserved heterogeneity.

Table 3.3 reports the estimated results of crop share elasticities with respect to expected prices and

yields and their respective risk measures. The first result that is worth noting is that all own-price

elasticities (values in bold) are positive and highly significant. For all the selected crops, the

expected price effects are inelastic. For example, one percent increase to the expected prices of

matooke, maize, and beans increases the expected land acreage shares of these crops by respectively

0.35 (0.32%), 0.44 (0.38%), 0.37 (0.31%) in the static (dynamic) model. The cross-price elasticities

are also significant at 1 percent level, all negative, and in most cases smaller than the own-price

acreage responses, implying crop substitution among Ugandan farmers concerning crop land

allocations.

Essay III

107

Table 3.3 Acreage elasticities of expected prices and yields and their related risks- Static vs Dynamic models

Matooke Cassava Maize Potatoes Beans Other cereals

Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic

Expected prices

1p 0.354*** 0.322*** -0.043*** -0.036*** -0.059*** -0.047*** -0.042*** -0.036*** -0.055*** -0.047*** -0.021*** -0.012***

2p -0.042*** -0.037*** 0.378*** 0.359*** -0.079*** -0.068*** -0.048*** -0.043*** -0.068*** -0.056*** -0.049*** -0.037***

3p -0.047*** -0.039*** -0.068*** -0.072*** 0.439*** 0.382*** -0.042*** -0.046*** -0.075*** -0.066*** -0.035*** -0.033***

4p -0.042*** -0.036*** -0.043*** -0.042*** -0.046*** -0.042*** 0.276*** 0.224*** -0.048*** -0.036*** -0.021*** -0.018***

5p -0.071*** -0.096*** -0.062*** -0.062*** -0.010*** -0.068*** -0.040*** -0.048*** 0.368*** 0.308*** -0.028*** -0.027***

6p -0.024*** -0.021*** -0.056*** -0.049*** -0.053*** -0.042*** -0.024*** -0.028*** -0.048*** -0.035*** 0.219*** 0.198***

Expected yields

1y 0.524*** 0.505*** -0.180*** -0.092*** -0.206*** -0.137*** -0.139*** -0.121*** -0.162*** -0.138*** -0.178*** -0.103***

2y -0.236 -0.198 0.698*** 0.469*** -0.148*** -0.104*** -0.108*** -0.088*** -0.155*** -0.069*** -0.125*** -0.116***

3y -0.184 -0.115 -0.094*** -0.059*** 1.037*** 0.723*** -0.181*** -0.138*** -0.180*** -0.168*** -0.075*** -0.068***

4y -0.177*** -0.150* -0.108*** -0.077*** -0.128*** -0.101*** 0.584*** 0.449*** -0.074*** -0.067*** -0.151*** -0.147***

5y -0.183 -0.146* -0.140*** -0.119*** -0.185*** -0.104*** -0.090*** -0.046*** 0.876*** 0.659*** -0.108*** -0.096***

6y -0.140*** -0.064* -0.073*** -0.055* -0.051*** -0.045** -0.045*** -0.037** -0.098*** -0.046* 0.756*** 0.640**

Price risks

1vp -0.007*** -0.025*** -0.012*** -0.025*** -0.007*** -0.005*** -0.003*** -0.005*** -0.007*** -0.015*** -0.005*** -0.005***

2vp -0.011*** -0.089*** -0.011*** -0.045*** -0.012*** -0.044*** -0.011*** -0.049*** -0.013*** -0.041*** -0.013*** -0.013***

3vp -0.006*** -0.030*** -0.005 -0.025*** -0.020*** -0.010*** -0.004 -0.020*** -0.006*** -0.030*** -0.007*** -0.035***

4vp -0.011*** -0.049*** -0.026*** -0.059*** -0.021*** -0.095*** -0.008*** -0.036*** -0.021*** -0.095*** -0.012*** -0.055***

5vp -0.001*** -0.005 -0.001*** -0.004 -0.006*** -0.029 -0.001 -0.004 -0.005*** -0.024** -0.009*** -0.043

6vp -0.011*** -0.028 -0.015*** -0.026 -0.008*** -0.041 -0.010*** -0.026 -0.010*** -0.025 -0.009*** -0.023*

Yield risks

1vy -0.087*** -0.102*** -0.052*** -0.094*** -0.050*** -0.074*** -0.042*** -0.077** -0.044*** -0.073*** -0.023*** -0.056**

2vy -0.098*** -0.115*** -0.047*** -0.063*** -0.048*** -0.058*** -0.325*** -0.053* -0.029*** -0.014* -0.027*** -0.073*

3vy -0.123** -0.133* -0.190*** -0.129* -0.176*** -0.162*** -0.134*** -0.107* -0.155*** -0.090* -0.080*** -0.060

4vy -0.150* -0.150** 0.047*** -0.134*** -0.045*** -0.109* -0.039*** -0.137*** 0.037*** 0.036* 0.022*** 0.050*

5vy -0.020** -0.050*** -0.050*** -0.039* -0.019* -0.019* 0.020 -0.019* -0.024** -0.048*** -0.025* -0.014*

6vy 0.045*** -0.015* 0.072 -0.026* -0.046*** -0.051*** -0.053*** -0.020* -0.069*** -0.010* -0.047** -0.020***

Note: ***, **, and * indicate coefficients statistically significant at 1, 5, and 10% levels, respectively.


108

This inelastic reaction of acreage shares to expected prices may be partially explained by crop-

specific agronomic constraints (Wu at al., 2004), crop interdependence since changes in the prices

of one crop also affect acreage decisions of other crops (Lacroix and Thomas, 2011), or market

failures (de Janvry et al., 1991).

Second, the impact of own expected yields on acreage shares is both positive and in all cases higher

than the corresponding price elasticities. Similar to price elasticities, maize displays the largest

coefficient (0.72), followed respectively by beans (0.66) and other cereals (0.64) in the dynamic

model. Cross-yield elasticities are all negative, confirming the substitutability nature of the selected

crops. These result patterns are consistent with the findings by Weersink et al. (2010) for Canadian

farmers who showed that expected yields had much higher effects on land acreage than expected

prices. The larger impact of yield expectations may be explained by the fact that most agricultural

households in Uganda are subsistence farmers or net buyers (Benson et al., 2008; see essay II).

Therefore, they place greater value on yields as large yields imply higher production and

subsequently more room for home consumption, while increases in the expected end-of-season

output prices are essentially more meaningful to farmers participating into food markets.

Third, price and yield risks also appear to be relevant determinants of land allocation decisions: the

more volatile the expected output prices or yields, the smaller the proportion of land the farmer will

be willing to share out between the selected competing crops. And similarly to the case of expected

values, farmers appear more sensitive to changes in yield risks than in price risks for all crops,

regardless of the model specification. Estimated elasticities associated with price risks are in most

cases less than 0.05% while yield risk elasticities are around 0.10%, reaching the highest levels for

maize (-0.18 and -0.16% in the static and dynamic models, respectively). Similar patterns were

found by Lin and Dismukes (2007), Weersink et al. (2010), Hung and Khanna (2010), and Liang et

al. (2011).

These various own- and cross- acreage elasticities can be further illustrated by simulating the effects

of simultaneous shocks to the expected prices and yields and their volatility across all crops. Table

3.4 shows these equiproportional elasticities computed by vertically summing the statistically

significant own- and cross- elasticities in table 3.3. The table reveals that a positive shock to all the

expected prices would increase the acreage shares of all selected crops in both the static and

dynamic specifications, although the effects are relatively larger in the static models. When the

simulated shocks originate from expected yields, the impacts are globally amplified. For instance,

the acreage shares towards maize would increase by 2.32% and 1.15% in case of a 10% positive

shock to the expected yields and prices of all crops, respectively. However, if a covariate shock

Essay III

109

would simultaneously increase the volatility of both prices and yields, it would become unattractive

to maintain previous cropping patterns given the shrinkage of the expected gross revenues.

Consequently, the estimated results suggest that farmers would allocate away from all the selected

crops.

Table 3.4 Equiproportional elasticities - Static vs Dynamic models


S D S D S D S D S D S D

ep 0.128 0.093 0.106 0.098 0.192 0.115 0.080 0.023 0.074 0.068 0.065 0.071

ey 0.207 0.145 0.103 0.067 0.319 0.232 0.021 0.019 0.207 0.171 0.119 0.110

evp -0.047 -0.193 -0.065 -0.154 -0.074 -0.154 -0.032 -0.110 -0.062 -0.250 -0.055 -0.131

evy -0.433 -0.565 -0.292 -0.483 -0.384 -0.473 -0.593 -0.413 -0.284 -0.199 -0.180 -0.113

Note: The letters S and D stand for the static and dynamic acreage share models, respectively. ep and ey

represent the equiproportional price and yield elasticities, while evp and evy are their risk elasticity counterparts.

In addition to expected prices and yields, climatic characteristics also play a key role in defining

crop acreage allocations. As suggested by the first part of table 3.5, the effects of changes in

average rainfall and temperature are mixed. Increases in average monthly rainfall positively affect

the shares of maize, potatoes and beans, while extreme temperatures are significantly detrimental

for all selected crops. The results further emphasize that it is the changes in the volatility rather

than in the mean values of the climatic variables that are more influential for land allocations.

Indeed, the impact of increased volatility in rainfall and temperature is significant at 1% for all

crops. Whereas the average temperature displays for instance a marginal effect in the dynamic

model, its volatility reduces expected crop shares by 0.09% for both cassava and other cereals and

0.16% for beans. These results are in line with findings by Arriagada (2005), Kurukulasuriya and

Mendelsohn (2008), Seo and Mendelsohn (2007, 2008) and Kaminski et al. (2013) who reported

that changes in climatic conditions push farmers to substitute away from agricultural activities. In

regards to land characteristics, the second part of table 3.5 indicates that only changes in total land

available and the proportion of good quality land positively and significantly influence the shares to

be allocated to different crops. The largest (smallest) impact of land size concerns cassava (maize)

with 0.14% (0.06%) and 0.11% (0.01%) in the dynamic and static models, respectively. Finally,

farmers’ characteristics have a negligible impact on acreage shares.


110

Table 3.5 Effects of agro-climatic variables and farmer’s characteristics


Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic Static Dynamic

Climatic characteristics

mar -0.108 -0.089 -0.023*** -0.014** 0.023*** 0.018** 0.024*** 0.020* 0.018*** 0.015** -0.014 -0.011

marcv -0.061*** -0.049*** -0.062*** -0.066*** -0.042*** -0.090*** -0.026*** -0.079*** -0.022*** -0.006*** -0.094*** -0.045***

dmt -0.025* -0.024* -0.012* -0.011* -0.024* -0.180* -0.096* -0.068** -0.035*** -0.027** -0.039* -0.034*

dmtcv -0.197*** -0.142 -0.138*** -0.089*** -0.179*** -0.103*** -0.189*** -0.157*** -0.158*** -0.160*** -0.087*** -0.089***

Farm characteristics

tld 0.108*** 0.082*** 0.113*** 0.135*** 0.007 0.058*** 0.102*** 0.068*** 0.054*** 0.087*** 0.055 0.077***

ldq 0.008*** 0.005* 0.033*** 0.006* 0.058*** 0.002** 0.034*** 0.056* 0.039*** 0.010** 0.055*** 0.011*

ldir 0.049 0.095 0.030 0.038 0.022 0.019 0.034 0.039 0.023 0.067 -0.099 -0.011

ldsp -0.017 -0.008 0.039 0.027 0.051 0.028 -0.011 -0.036 0.054 0.018 0.011 -0.027

Farmer’s characteristics

educ 0.000 0.001 0.000 0.000 0.001 0.000 0.001 0.000 0.000 0.001 0.000 0.000

age -0.014 -0.021* 0.013 -0.005 -0.006 -0.019 0.014 0.006 0.014 0.001 0.019 0.009

sex 0.014 0.011 0.003 -0.004 -0.001 -0.004 -0.003 -0.009 0.000 -0.006 0.003 -0.004

hsz 0.015*** 0.070* 0.019*** 0.020* 0.002*** 0.070* 0.007*** 0.009** 0.010*** 0.010* 0.011*** 0.013*

Note: ***, **, and * indicate coefficients statistically significant at 1% , 5%, and 10% levels, respectively.

111

3.6 Predictability performance

To assess the quality of the estimation results and their predictability performance, I compare for

each farmer the actual and predicted crop shares obtained from acreage share models and test for

the significance of these differences. Table 3.6 shows a comparison between observed ks and

predicted ks acreage shares.

Table 3.6 Observed versus predicted acreage shares

Static model Dynamic model

ks ks ks kk ss ˆ/ Equality

test ks ks kk ss ˆ/ Equality

test

2009/10

1k 0.118

(0.195)

0.146

(0.135)

0.028

(0.128)

0.192 4.729

[0.006]***

0.120

(0.158)

0.002

(0.112)

0.017 0.367

[0.006)]

2k 0.165

(0.213)

0.186

(0.127)

0.021

(0.150)

0.113 3.427

[0.005]***

0.171

(0.152)

0.006

(0.142)

0.035 0.901

[0.007]

3k 0.144

(0.186)

0.157

(0.113)

0.012

(0.129)

0.076 2.264

[0.005]**

0.149

(0.135)

0.006

(0.119)

0.040 0.963

[0.006]

4k 0.092

(0.142)

0.114

(0.090)

0.021

(0.101)

0.184 5.067

[0.004]***

0.096

(0.104)

0.004

(0.095)

0.041 0.935

[0.004]

5k 0.134

(0.163)

0.147

(0.100)

0.013

(0.115)

0.088 2.803

[0.005]***

0.138

(0.119)

0.004

(0.109)

0.029 0.787

[0.005]

6k 0.100

(0.175)

0.128

(0.122)

0.027

(0.114)

0.211 5.179

[0.005]***

0.104

(0.143)

0.004

(0.108)

0.038 0.672

[0.006]

2010/11

1k 0.122

(0.193)

0.152

(0.133)

0.030

(0.131)

0.197 5.140

[0.006]***

0.125

(0.153)

0.003

(0.121)

0.024 0.449

[0.006]

2k 0.164

(0.201)

0.196

(0.129)

0.031

(0.144)

0.158 5.147

[0.006]***

0.174

(0.147)

0.008

(0.144)

0.046 1.341

[0.006]*

3k 0.113

(0.157)

0.136

(0.099)

0.023

(0.116)

0.169 5.053

[0.005]***

0.121

(0.114)

0.009

(0.109)

0.074 1.816

[0.005]*

4k 0.083

(0.125)

0.108

(0.085)

0.025

(0.088)

0.231 6.550

[0.004]***

0.088

(0.094)

0.005

(0.086)

0.057 1.371

[0.004]*

5k 0.123

(0.152)

0.147

(0.097)

0.024

(0.112)

0.163 5.245

[0.005]***

0.128

(0.108)

0.005

(0.108)

0.038 1.001

[0.005]

6k 0.075

(0.151)

0.112

(0.112)

0.036

(0.103)

0.245 7.726

[0.005]***

0.079

(0.124)

0.003

(0.093)

0.039 0.692

[0.005]

2011/12

1k 0.120

(0.182)

0.150

(0.126)

0.030

(0.121)

0.200 5.430

[0.006]***

0.122

(0.149)

0.002

(0.114)

0.016 0.407

[0.006]

2k 0.130

(0.172)

0.158

(0.107)

0.028

(0.122)

0.177 5.550

[0.005]***

0.138

(0.125)

0.008

(0.122)

0.058 1.466

[0.005]*

3k 0.121

(0.155)

0.139

(0.100)

0.017

(0.112)

0.122 3.726

[0.005]***

0.128

(0.117)

0.007

(0.104)

0.055 1.346

[0.005]*

4k 0.084

(0.121)

0.108

(0.084)

0.024

(0.083)

0.222 6.651

[0.004]***

0.086

(0.095)

0.003

(0.082)

0.037 0.672

[0.004]

5k 0.132

(0.152)

0.149

(0.093)

0.017

(0.112)

0.114 3.779

[0.004]***

0.136

(0.111)

0.005

(0.110)

0.035 0.989

[0.005]

6k 0.074

(0.144)

0105

(0.108)

0.031

(0.096)

0.295 6.947

[0.005]***

0.076

(0.122)

0.003

(0.088)

0.039 0.692

[0.005]

Note: 1k , 2k , 3k , 4k , 5k , and 6k refer respectively to matooke¸ cassava, maize, potatoes, beans, and other cereals. The

equality test is a t-test with unequal variances checking whether the mean predicted shares are significantly different

from the mean observed shares. kkk sss ˆ . Standard deviations and standard errors are reported into parentheses

and into brackets, respectively. ***, **, and * indicate coefficients statistically significant at 1% , 5%, and 10% levels,

respectively.


112

The columns ks and kk ss ˆ/ give the absolute and relative differences between the two sets of

acreage shares for panel waves 2009/10, 2010/11, and 2011/12.

The first conclusion is that the static share model performs poorly in terms of prediction of the

acreages to allocate to different crops. All the expected shares are significantly overstated for each

crop and in each panel wave. The mis-prediction occurs mostly with regards to potatoes and other

cereals. For example, in 2009/10, the differences were the smallest for maize (7.6%) and beans

(8.8%) but very large for other cereals (21.1%) and potatoes (18.4%). Second, when past crop

choices and initial conditions are accounted for, the predictability performance of the model is

significantly improved. Indeed, in the dynamic model, the acreage shares are remarkably well

predicted with the deviations from the actual shares being on average of less than 5% and globally

not significant. In general, the dynamic share model appears more accurate for matooke and beans.

The second performance test consists in analyzing how well the estimated results predict the

optimal crop choice. To that end, I define for each farmer in a given year the optimal crop choice as

the crop yielding the highest expected profit using the predicted shares. However, in the surveys,

data on input values and quantities are collected at the plot/parcel level, with no details on how they

are allocated to different crops. To obtain crop-specific input allocations, I follow the behavioral

approach proposed by Just et al. (1990) to estimate input allocations in multicrop farms. It consists

in estimating a system of input allocation equations as a function of crop acreage shares, regional

and time dummies. More specifically, I estimate the following linear model with Seemingly

Unrelated Regression (SUR):

Iiisx

K

k

ihthkthktiht ,...,,

1

Zγ'D'βD'β 2211 ,

where ihtx is the total expenditure on variable input Iii ,...,1, by farmer h at time t. ihtx contains

farmers’ real expendiures on hired labor, seeds, fertilizer, and pesticides. hkts is the acreage share

allocated to crop k; 1D and 2D are vectors of regional and time dummies; Z is a vector of farmers’

characteristics (such as age, sex, and education of the household’s head). hkt , 1β , 2β , and γ are

unknown parameters to be estimated; iht is the error term assumed normally and identically

distributed. The estimated parameters hkt are then multiplied by the land allocated by the farmer to

each crop hthkt Ls * to get crop-specific allocation of input i.

In table 3.7, the third column (“obs.”) gives for each crop the number of farmers whose optimal

crop choice is actually 6,...,1, iki . Each cell in the static and dynamic models provides the

percent of (in)correct predictions, with the main diagonals (values in bold) showing the proportion

(3.25)

113

of correct predictions. For example, in 2009/10, among the 167 farmers whose matooke ( 1k ) was

actually the optimal crop choice, the static share model correctly identifies 25.7% of them (43

farmers) and erroneously predicts that 43.7, 10.8, and 19.8% of them will have maize, potatoes,

and beans as optimal choices.

Table 3.7 Comparison between predicted and observed optimal crop choice

Observed

optimal crop

Predicted optimal crop choice

Static model Dynamic model

crop Obs. 1k 2k 3k 4k 5k 6k 1k 2k 3k 4k 5k 6k

2009/10

1k 167 0.257 0.000 0.437 0.108 0.198 0.000 0.431 0.012 0.323 0.048 0.186 0.000

2k 256 0.004 0.379 0.527 0.070 0.016 0.004 0.000 0.508 0.379 0.066 0.047 0.000

3k 598 0.000 0.002 0.987 0.010 0.000 0.002 0.012 0.003 0.968 0.007 0.010 0.000

4k 242 0.008 0.020 0.446 0.512 0.012 0.000 0.049 0.033 0.306 0.591 0.020 0.000

5k 276 0.011 0.011 0.536 0.101 0.341 0.000 0.029 0.014 0.377 0.065 0.511 0.004

6k 52 0.000 0.058 0.481 0.250 0.115 0.096 0.019 0.058 0.327 0.135 0.173 0.288

2010/11

1k 56 0.036 0.071 0.732 0.107 0.054 0.000 0.643 0.054 0.107 0.107 0.089 0.000

2k 406 0.000 0.527 0.461 0.002 0.010 0.000 0.000 0.613 0.352 0.005 0.029 0.000

3k 696 0.000 0.007 0.993 0.000 0.000 0.000 0.000 0.013 0.980 0.001 0.006 0.000

4k 140 0.000 0.086 0.550 0.264 0.100 0.000 0.007 0.107 0.343 0.543 0.000 0.000

5k 279 0.000 0.122 0.452 0.011 0.416 0.000 0.000 0.082 0.330 0.025 0.563 0.000

6k 18 0.000 0.778 0.222 0.000 0.000 0.000 0.000 0.111 0.278 0.000 0.000 0.611

2011/12

1k 62 0.032 0.032 0.290 0.048 0.597 0.000 0.629 0.065 0.065 0.249 0.000 0.000

2k 322 0.000 0.422 0.466 0.022 0.090 0.000 0.000 0.612 0.298 0.012 0.078 0.000

3k 648 0.002 0.009 0.969 0.005 0.015 0.000 0.000 0.009 0.971 0.003 0.017 0.000

4k 169 0.000 0.047 0.485 0.207 0.260 0.000 0.000 0.041 0.266 0.692 0.000 0.000

5k 365 0.000 0.019 0.384 0.005 0.592 0.000 0.000 0.044 0.285 0.011 0.660 0.000

6k 27 0.000 0.148 0.786 0.000 0.036 0.000 0.000 0.000 0.222 0.000 0.000 0.778

Note: 1k , 2k , 3k , 4k , 5k , and 6k refer respectively to matooke¸ casssava, maize, potatoes, beans, and other cereals

From table 3.7, it appears that the overall predictive power of the static model is relatively weak.

The model performs exceptionally well only with respect to maize ( 3k ) with nearly 100% of correct

predictions. For the remaining crops, the proportions of exact predictions are globally low. In

2010/11 and 2011/12, the static model even falls to correctly identify a single farmer concerning the

choice of other cereals. In contrast, the dynamic model presents a relatively improved prediction

power for all crops. On average, its predictions are accurate in more than 50% of cases and are

greater than those from the static model. The differences between these two models are particularly

striking with respect to matooke and other cereals (in 2010/11 and 2011/12).


114

3.7 Conclusions

This study has used farm- and crop-level data of Ugandan agricultural households to understand the

relative importance of perceived agricultural and market risks on farmers’ crop choices and acreage

decisions. It proposes a theoretical model in which a representative farmer optimally chooses the

land shares to allocate to different crops in order to maximize the expected utility of profit. The

underpinning theoretical model is then translated into two related specifications of farmers’ crop

decisions: a multivariate selection model and an acreage share model. The former describes how the

farmer decides which crop(s) to grow while the latter models how he allocates his land area to

different crops conditional on crop selection. All these models take account of two important facets

of the farmer’s behavior: the possibility of state dependence and spillover (or rotational) effects

through the incorporation of past crop choices and land allocations, and the presence of unobserved

heterogeneity in the farmer’s decision process. The models are applied to a balanced panel of 1,598

farmers, first interviewed in 2005/6 by the Uganda Bureau of Statistics (UBoS) and then followed

successively in 2009/10, 2010/11 and 2011/12.

The results provide evidence of both strong state dependence and significant spillover effects in

farmers’ crop choices and area allocations. This means that, although Ugandan farmers tend to

reproduce their previous land distributional patterns (positive own state dependence), they are also

likely to adjust their choices to take advantages of rotational effects (negative cross-state

dependence) or changes in relative crop profitability. In terms of risks and expectations, both the

multivariate crop selection and acreage share models agree on the crucial role played by farmers’

expectations of market prices, yield levels and their variability (captured by price and yield risks),

on the one hand, and rainfall and temperature variability, on the other. They suggest that expected

own prices and yields positively influence the likelihood of crop selection and land shares while

their variability stresses a risk-averse behavior from Ugandan farmers. They finally show that

changes in weather variability (in terms of coefficients of variation of rainfall and temperature) are

likely to impact more on crop selection and land allocations than changes in their average values.

115

Essay IV

Welfare growth, poverty traps, and differential exposure to food price

shocks

Evidence from Uganda

4.1 Introduction

Eradicating poverty has always been one of key challenges for and earliest objectives of national

policymakers and international agencies. Although at the global level, the Millennium Development

Goal (MDG) of halving extreme poverty (proportion of people living with less than 1$ a day) has

been achieved since 2010 (UN, 2014), some regions, particularly in Southern Asia and Sub-Saharan

Africa (SSA), are still lagging behind and will not probably meet the target by 2015 (World Bank,

2013). More than in any other regions of the world, populations in SSA are not only among the

most vulnerable to shocks and stressors (such as droughts, floods, or livestock and other asset

losses) but also face multiple failures in land, credit, and insurance markets (Barrett and Carter,

2013) which make them largely dependent on donor and humanitarian assistance to make their ends

meet. Recent research on poverty has thus advocated the need to study the underlying welfare

dynamics in order to better understand the process through which some individuals or households

may fall into or climb out of poverty (Naschold, 2005, 2013).

Particularly, a bourgeoning empirical literature on the intertemporal dynamics of poverty focuses on

the existence of poverty traps, broadly defined as “(…) any self-reinforcing mechanism which

causes poverty to persist” (Azariadis and Stachurski, 2005: 326). At the core of the poverty trap’s

literature lie three interrelated concepts, namely the presence of critical thresholds preventing

people to move from one welfare path onto another (Barrett and Carter, 2013), the occurrence of

shocks, either permanent or temporary, likely to push people at a low-level stable equilibrium from

which they cannot escape without an important positive shock to their welfare (Van Campenhout

and Dercon, 2012), and the existence of a single or multiple equilibria (Carter and Barrett, 2006).

The existence of these traps of poverty is an empirical matter. While some studies (Lybbert et al.,

2004; Adato et al., 2006; Barrett et al., 2006; Amare and Waibel, 2013) find evidence in support for

Essay IV

116

poverty traps, the results of others (Jalan and Ravallion 2002; Lokshin and Ravallion 2004; Antman

and McKenzie 2005; Naschold, 2013, among others) suggest the absence of any poverty trap. If

poverty traps do exist, then their identification and location become crucial for the implementation

of appropriate policies likely to lift households from persistent poverty zones to desirably higher

and self-sustained well-being equilibrium (Dutta, 2014).

Accordingly, the last essay examines households’ welfare pathways to identify the links between

shocks’ occurrences and poverty traps. More precisely, it studies traps and identifies potential

critical thresholds to determine whether households’ welfare dynamics are characterized by a single

or multiple equilibria. In the analysis, the emphasis is put on household consumption and assets,

rather than on income, which generally suffers from important measurement errors, particularly in

developing countries, and is more prone to stochastic movements and sensitive to transitory

disturbances likely to generate false positives and false negatives in regards to poverty traps (Barrett

et al., 2006). This choice has also the advantage of enriching welfare analyses by decomposing poor

into subgroups of stochastically and structurally poor - depending on the levels of household assets

and their consumption levels - and by investigating whether these two groups are significantly

different in their likelihood of being trapped into poverty.

The evidence shown in this study contributes to the existing literature on shocks, welfare dynamics,

and poverty traps in two ways. First, I lay emphasis on and investigate the link between instabilities

in commodities’ prices and the existence of poverty traps. Indeed, in many SSA countries, the

majority of the population earns their income from agricultural activities, intrinsically very sensitive

to changes in crop market prices. While numerous studies have raised widespread concern that the

recent global food price crisis might have pushed millions of population into poverty (Cudjoe et al.,

2008; Headey and Fan, 2008; Ivanic and Martin, 2008; Boysen, 2009; Hella et al., 2011; Vu and

Glewwe, 2011; Ferreira et al., 2011), they all fall short of evaluating the extent to which some

households have fallen into chronic poverty or have been caught into poverty traps as a result of

such price shocks. Built upon a modified standard optimal growth model (Geromini et al., 2006)

allowing for reference-dependent preferences (Köszegi and Rabin, 2006) and a measure of

household’s exposure to food price instabilities (Collier and Dehn, 2001; Dehn, 2001; Combes et

al., 2012), I show that food price shocks may lead to a lower equilibrium and therefore reinforce the

persistence of poverty for those already thrust into a trap.

The Ugandan context is particularly germane for this empirical analysis for two main reasons. On

the one hand, its poverty profiles are heterogeneous across regions and between rural and urban

areas. In fact, although Uganda is generally praised for its economic performance characterized by a


117

growth rate of Gross Domestic Product (GDP) well above that of the SSA77

, its economy has been

accompanied by rising inequality between rural and urban areas and across different geographical

regions. For instance, while the share of poor households living in rural areas increases from 26.7%

in 2009/10 to 31.2% in 2010/11, the proportion of urban poor decreased from 11% to 7% during the

same period (UBoS, 2013). Spatially, poverty rates were the highest in the Northern and Eastern

regions with respectively 38.9 and 36.8% in 2010/11 against only 1% in Kampala (UBoS, 2013).

On the other hand, the household panel dataset used in this study not only includes a large number

of observations (around 2,200 households per survey), has detailed information on assets, income,

or consumption expenditures, but also covers periods of stable and large food price changes,

suitable for analyzing the impact of price instabilities.

Second, the paper uses a battery of econometric techniques to check whether the identified welfare

pathways are genuine dynamics or instead an artifact of the specific estimation method used

(Naschold, 2013). By means of parametric methods (System-GMM and cubic polynomial

regression models), non-parametric methods (locally weighted scatterplot smoother (LOWESS) and

local polynomial regression with Epanechnikov kernel weights), and semi-parametric methods

(Ruppert et al.’s penalized splines estimators), I identify critical welfare thresholds, test for the

presence of poverty traps in Uganda, and check for their robustness to model specifications.

This study is organized as follows. The next section presents a brief literature review on the links

between shocks, welfare dynamics and poverty traps. Section 3 summarizes existing empirical

evidence pertaining to micro-level poverty traps. In Section 4, a modified consumption growth

model is presented and its theoretical implications are discussed. Section 5 describes the dataset

used for the empirical analysis with a particular emphasis on the construction of a food price shock

variable and household’s asset index. In section 6, different estimation methods are discussed and

empirical results are presented. Section 7 concludes the study.

4.2 Literature review: shocks, welfare dynamics, and poverty traps

In recent years, the analysis of welfare dynamics over time has gained prominence in development

economics’ circles. The heed has been particularly put on the reasons why some individuals or

households manage to lift themselves permanently out of poverty, while others still remain mired

into poverty for an extended period of time. Of particular interest is the vulnerability of individuals

or households to idiosyncratic and covariate shocks. Indeed, researchers have explored the

mechanisms through which the occurrence of such shocks may induce a profound modification of

77

The Uganda’s GPD grew from 5.9 percent in 2009/10 to 6.7 percent in 2010/11 (UBOS, 2012), while that of Sub-Saharan Africa decreased from 5.2 to 3.9% during the same period.

Essay IV

118

the welfare accumulation dynamics (in terms for example of income, consumption, or assets) and

potentially lead to poverty persistence and poverty traps. For example, climate shocks, associated

with extreme weather conditions (e.g., droughts, floods, cyclones) may overnight bring households’

assets to a level below which accumulation growth becomes impossible without a substantial

external push (Giesbert and Schindler, 2012). In rural areas of many developing countries, weather-

related disasters (insufficient rainfall, extreme temperatures, droughts, etc) may have catastrophic

consequences on crop production and therefore on farm revenues. For example, Carter et al. (2007)

found evidence that short-term asset shocks (hurricane in Honduras) and long-term income shocks

(drought in Ethiopia) were responsible of people being trapped into poverty.

The concept of poverty traps originates from macro-economic literature on growth dynamics

through three hypotheses. The first is the idea of unconditional convergence according to which all

households will follow the same welfare equilibrium path and will ultimately converge to a unique

living standard and asset stock. In this Solow-type growth model, any shock will only temporarily

modify the welfare dynamics, without preventing the convergence towards the equilibrium to occur

(Geromini et al., 2006). Under the conditional convergence hypothesis, dating back to Baumol

(1986) and DeLong (1988), there are as many welfare pathways as there are groups or clubs of

individuals sharing some intrinsic characteristics (agro-ecological conditions, natural resource

endowments, ethnic diversity, innate abilities and skills, etc). Depending on their characteristics,

some groups will face a low-level equilibrium from which they cannot escape and move to a higher

equilibrium level. The last hypothesis posits the prevalence of multiple equilibria, with at least one

associated with a poor standard of living and another with a high level of well-being (Carter and

Barrett, 2006). In this context, poverty trap is characterized by the existence of critical thresholds,

with at least one threshold, once crossed, leads to poverty exit and welfare accumulation and below

which depletion occurs (Barrett et al., 2007; Kraay and McKenzie, 2014).

Theoretically, the economics literature identifies at least three structural causes of multiple

equilibrium poverty traps, playing at different scales: “big push” theories of development,

originated from Rosenstein-Rodan (1943); physical work capacity theories (Dasgupta 1993, 1997);

and incomplete and missing markets (Barrett and Carter, 2013)

The first theoretical argument for poverty traps stems from the concept of “big push” that

emphasizes the necessity of coordinated investments as a basis to industrialization. When many

different sectors of an economy simultaneously adopt increasing returns technologies or when the

economy allocates most of its resources to the increasing returns sectors, then wages will be high in

all sectors, creating more income and demand for goods which in turn will enlarge the market,


119

leading to industrialization. Conversely, the allocation of resources to constant returns sectors will

result in low wage levels across sectors and demand reductions (Kraay and McKenzie, 2014). On

the other hand, the “big push” model can also be associated with coordination failures between

firms wherein agents only mimic the economic behavior of their peers by deciding whether to

invest or not depending on their expectations of what other agents will do. In this case, poverty trap

occurs when all agents fail to invest in the efficient technology.

The second widely developed cause of poverty trap assumes a non-linear relationship between

individual physical work capacity and his nutritional or food intake status. In this model, labor

productivity and wage depend solely on consumption and income is entirely derived from labor

market (Van Campehnout and Dercon, 2012). The underlying idea is that poverty will beget poverty

or be self-reinforcing insofar as poor households will not have enough resources to increase the

quantity and quality of their food intake. They will become too undernourished to either participate

productively into the labor market (from which they are thus rationed) or earn enough (and

therefore consume enough) to help them climb out of nutritional poverty traps. As long as

consumption will be below a certain threshold, the worker will remain unproductive and will thus

be trapped into poverty.

Finally, uninsured risks and incomplete credit and other financial markets can give rise to poverty

traps’ mechanisms, particularly in developing countries where households often have limited access

to capital and insurance markets. From this perspective, shocks can have disproportionally

permanent consequences on welfare accumulation, trigger irreversible mechanisms for individuals

already close to the poverty line, and keep poor households from climbing out of poverty (McPeak

and Barrett, 2001; Dercon, 2005; Krishna, 2006). Ex ante management strategies to risk exposure

and ex post mitigation mechanisms may also lead to poverty traps. To manage risk exposure, poor

households may choose a diversified portfolio comprised of low-risk activities but at the expense of

asset returns, reinforcing the likelihood of being trapped into poverty. For example, Bezabih et al.

(2011) found that in Ethiopia crop portfolio choice was essentially influenced by rainfall variability

and that farmers were likely to choose less risky crops at the expense of high returns. Ex post,

empirical evidence indicates that poor households often sell out their meager assets, principally

livestock, to cope with shocks and smooth their consumption, thereby exacerbating their already-

unsustainable welfare conditions. In some other circumstances, empirical findings suggest that poor

may instead opt for asset smoothing by reducing their consumption or healthcare expenditures or

withdrawing children from school, resulting in health and education deficiencies and potential

Essay IV

120

intergenerational transmission of poverty (Hoddinott, 2006; Carter et al., 2007; Amare and Waibel,

2013).

4.3 Empirical evidence on poverty traps

Over the last two decades, empirical research that has concentrated on the identification of poverty

traps and the existence of single or multiple welfare equilibria has obtained mixed results. For

example, using a six-year panel of income from rural Chinese provinces, Jalan and Ravallion (2002)

find evidence of a geographical poverty trap, implying that well-endowed areas enjoy consumption

levels rising over time, while households trapped into geographic poverty are stuck into a lower

standard of living. Lokshin and Ravallion (2004) analyze nonlinearities of household income in the

presence of endogenous attrition using a four-year household panel from Russia and a six-year

panel from Hungary. By means of a semi-parametric Full Information Maximum Likelihood

(FIML), they find evidence of nonlinearities in income dynamics but fail to find a dynamic poverty

trap.

Lybbert et al. (2004) use 17-year cattle herd histories collected among pastoralists in southern

Ethiopia to study stochastic livestock dynamics. They apply a Nadaraya-Watson estimator of

bivariate case using Epanechnikov kernel with an arbitrary bandwidth of 1.5 and find evidence of

multiple dynamic wealth equilibria among pastoralists. Particularly, they find that households with

herd size less than 15 heads fall into a sedentarisation zone, while households with more than 15

head converge to an upper equilibrium of about 75. Above this level, accumulation becomes too

costly to be sustainable.

Adato et al. (2006), Carter and Barrett (2006); Barrett et al. (2006), Quisumbing and Baulch (2009)

Naschold (2009; 2013), Giesbert and Schindler (2012), Amare and Waibel (2013) all look at

poverty trap from an asset-based perspective and derive asset-based wellbeing indices through

either a regression of expenditure/income on the household's productive assets or a factor analysis.

Specifically, Carter and Barrett (2006) argue that an asset-based approach to poverty trap enables

the researcher to distinguish persistent or structural poverty from stochastic poverty. Using a

livelihood-weighted approach to compute an asset index, Adato et al. (2006) and Amare and Waibel

(2013) find an S-shaped asset accumulation process and evidence of poverty traps in South-Africa

and rural Vietnam, respectively. Barrett et al. (2006) study welfare dynamics in rural Kenya and

Madagascar. They use qualitative and quantitative evidence to see what causes persistent poverty.

They find evidence of S-shaped asset dynamics using both non-parametric regressions and a fourth

order polynomial regression. On the other hand, Naschold (2009, 2013), Quisumbing and Baulch


121

(2009), Giesbert and Schindler (2012), have not found evidence for multiple equilibria but rather a

single stable state at a low level of well-being around the poverty line towards which everyone

converges.

Van Campenhout and Dercon (2012) explore the existence of livestock asset poverty traps in

Ethiopia using the Ethiopia Rural Household Survey (ERHS) from round 1 to round 6. Using a

GMM estimation and Threshold Auto-Regression model proposed by Hansen (1999; 2000), they

find nonlinearities in the dynamics of Tropical Livestock Units (TLUs) and multiple equilibria of

TLUs. When estimating the speed of convergence towards the low and high equilibria, they find

that the convergence to the former was almost twice as fast as convergence towards the latter.

Kwak and Smith (2010) and Dutta (2014) test for the existence of both single and simultaneous

poverty traps in Ethiopia and India, respectively. Using a range of econometric (parametric, non-

and semi-parametric) methods to the Ethiopia Rural Household Survey (ERHS) from 1994 to 2004,

Kwak and Smith (2010) identify only a single stable welfare equilibrium when using the full panel

sample but two equilibria when they split the data into two time intervals (1994-1999 and 1999-

2004). Moreover, their results suggest that households with chronic undernourishment and illiteracy

are trapped into lower equilibria while richer households enjoy high level of asset equilibrium.

Finally, Dutta (2014) uses the local polynomial regression with Epanechnikov kernel weights to test

the existence of multiple equilibria in asset poverty dynamics and a partial linear mixed model to

investigate the impact of under-nutrition and illiteracy on asset accumulation process in India. He

finds evidence of a single dynamic asset equilibrium across rural households but multiple traps

(asset, under-nutrition and illiteracy traps) in most depraved States.

4.4 Conceptual model

This study focuses on the analysis of consumption growth, assets accumulation, and the

identification of household-level poverty traps in an intertemporal framework where heterogeneous

economic agents are maximizing their welfare and accumulating assets. As in Jalan and Ravallion

(2002), and Elbers et al. (2002), I use a variant of the Ramsey growth model of consumption.

However, in the present model, I am explicitly allowing agents (households) to face two types of

shocks that directly affect their wealth accumulation: food price shocks fht , through their impact on

consumption levels and therefore household utility, and asset shockskht , through their effects on

income levels.

Concretely, let the consumption level and capital/asset stock of a utility-maximizing household h

for period t be htc and htk , respectively. For simplicity, I assume that the distributions of fht and

Essay IV

122

kht are independent of each other and across time and their respective cumulative density functions

denoted by .f and .k

are known by the household when he decides on htc and 1htk . The

relation between food price shocks and household consumption choices can be understood as

follows: at the beginning of each period t, the household forms his expectations about both the

probability of experiencing a price shock during period t and the magnitude of the shock given the

information set at his disposal (current and past food price levels), expectations about future levels

of food prices, and other constraints (labor, budget, or farm constraints). At the end of time t, after

the realization or not of fht , the household adapts his period t+1 decisions accordingly.

Formally, let .u be the instantaneous household’s utility function, twice differentiable, strictly

increasing, and strictly concave 0.'';0.' uu . To incorporate the effect of a food price shock

into the analysis, I assume, along the lines of Köszegi and Rabin (2006), that a household’s utility

depends on both the consumption bundle, c, and the realization or not of a food price shock fz ,

such that ff zccucU ; , where cu is an intrinsic consumption utility and fzc

is the utility gap or “gain-loss utility” function due to the realization of fht . The utility-gap function

is given by ff zcucuvzc , with 01 fzc , meaning that, in the absence of a

price shock, 1f and fcU ; reduces to the standard instantaneous utility function cu .

In terms of assets, the decision-maker accumulates a stock of assets at the end of each period t, 1tk ,

with a depreciation rate , assumed constant over time. Unlike in the standard Ramsey model, the

household assets are also exposed to shocks k .

Each household h maximizes his expected lifetime utility and solves the following optimization

problem:

0

0,

;1 t

ftttt

tf

kczcucucucUMax

tt

Ε

subject to

tttktt ckkfk 11

0k given

where 0Ε is the conditional expectation 00 ΨΕ with 0Ψ the household’s information set

available at time 0; 1,0 is the time discount factor. Similarly to food price shocks, when 1k

, there is no asset shock while 1k implies a negative shock that depletes part of the household

(4.1)


123

assets (Barrett et al., 2008). The value function derived from this problem in the presence of both

food price and asset shocks can be defined as:

tttktt

ts

fssss

st

ct ckkfktszcucucuMaxktV

st

1., 1Ε

The Bellman’s principle of optimality associated with the value function in (4.2) for each t = 0,

1,2,… gives the following result:

ttt

k

tt

f

tttt

t

ct ckkftVzcucucuMaxktV

tt

1,1, Ε

It is straightforward to show that the first order conditions derived from the stochastic Bellman

equation in (4.3) give the following Euler equation78

:

f

ttt

f

ttt

t

f

ttt

f

tttt

tk

tt

zcucucgcu

zcucucgcukf

'';''

'';''1' 1111111

1

1

Ε

where f

ttt

f

tt zcucucg ;

The Euler equation (4.4) equates the discounted marginal benefit of consumption in period t under

exposure to food price shock ft to the marginal cost, measured by the discounted marginal

expected utility of potential consumption foregone in period t+1. The Euler equation (4.4) can be

rearranged to give:

1';'

;'11

11

tktf

ttt

ftt kf

cU

cU

Ε

where

fttt

fttt

ftt zcucucgcucU '';'';'

and

fttt

fttt

ftt zcucucgcucU 11111111 '';'';'

78

This equation is obtained using the following Bellman-type equation obtained by maximizing (4.3):

tc

tc

tk

tc

tc

tkt

,

,

1,

1,

1,

1,

Ε , where the subscripts k and c denote partial derivatives, and

f

tttt

t zcucucu . , and tttkt ckkf 1.

(4.3)

(4.4)

(4.5)

(4.6)

(4.7)

(4.2)

Essay IV

124

The left-hand side of (4.5) represents the intertemporal marginal rate of substitution in consumption

under price instabilities, while the right-hand side is the marginal rate of transformation in

production (MRT) when assets are subject to shocks. Accordingly, the Euler equation (4.5) provides

two key messages regarding the effects of food price and asset shocks on household’s intertemporal

optimization problem. First, if exposure to food price shocks has no effect on household’s

consumption behavior (for example, in the case of autarkic households who do not participate into a

food market, tzcucucg fttt

ftt ,0; , tcucU t

ftt ,';' ), and assets are not

affected by shocks ( 1k ), the left-hand side of equation (4.5) reduces to a standard Euler

equation.

Second, if instead tzcucu fttt , , in other words, if food price shocks push a household to

modify his consumption behavior (think for example of pure consumers, net sellers, or net buyers of

agricultural products), then the marginal utility of consumption under ft becomes:

tcucgvzcucgvcucU tf

ttf

ttf

tttf

tt ,';'';'1';'

Hence, from equation (4.8), it is possible to get for some households tf

tt czc while for others

tf

tt czc , depending on their initial characteristics, attitude towards risk, preferences, or

expectations about the future. Particularly, when tf

tt czc , a price shock, either its realization or

household’s anticipation about its future realization, reduces the level of consumption that the

household would have achieved (attainable well-being). Repeated price shocks over time may thus

trigger downward welfare spirals and increase the likelihood of a poverty trap, unless the household

luckily receives a positive income shock (social transfers, inheritances, job opportunities…) or

policy interventions modify these price dynamics. Furthermore, in the presence of negative asset

shocks 1k , the standard marginal rate of transformation in output will be reduced the larger the

magnitude of the asset shocks.

To uncover the expression of the growth path of consumption 1lnlnln ttt ccc , let us assume

that the level of consumption under food price shocks is proportional to the importance of the shock

such that

t

ft

ftt cucU

; , where is a time-constant and household-specific elasticity that

captures the magnitude of the price shock. Furthermore, let the utility cu be represented by a

(4.8)


125

Constant Relative Risk Aversion (CRRA) utility function:

1

1ccu if 1,0 and

)ln(ccu if 1 ; with a measure of the degree of relative risk aversion. This implies that

tf

tf

tt ccU1

;' and

1

1

111;' tf

tf

tt ccU . Expressing the Euler equation in (4.5)

one period backwards and linearizing the resulting intertemporal marginal rate of consumption

substitution, we get the following expression of the growth rate of consumption between t and t-1:

1'ln11

ln1

ln1

ln1

lnln

11

tktf

t

ft

t

tt kf

c

cc

Equation (4.9), which will serve as the starting point to our empirical model, gives the consumption

growth path when both food price and asset shocks are allowed to co-exist. It shows that the

consumption path over time is affected not only by taste and preference shifters (time preference

and degree of risk aversion ) or marginal productivity of capital/assets net of depreciation rate

(last term of 4.9) but also by the magnitude of relative changes in food price shocks f

t

ftf

t

1

and capital/asset shockskt . In reduced form, equation (4.9) leads to the following specification:

hthhhtkt

fhtht

ht

htht XXZXZ

c

cc

543210

1

ln,lnlnln

where htZ is a vector of variables affecting taste and other preference shifters, htX and hX are

vectors of time-varying and time-invariant variables that influence household’s asset levels and

their marginal productivity; h is the household-specific unobserved heterogeneity capturing

household fixed effects; ht is the error term; i are unknown parameters to be estimated.

Importantly, 2 measures the impact of variations in differential exposure to food price shocks on

contemporaneous consumption growth, after controlling for other types of shocks, household

characteristics, or unobserved heterogeneity. In particular, a negative coefficient of 2 will be

indicative of consumption depletion consecutive to increases in the rate of exposure to price shocks,

all other things equal.

4.5 Data

This last essay uses a four-wave panel dataset of the Uganda National Panel Surveys (UNPS)

conducted in 2005/6, 2009/10, 2010/11, and 2011/2012 by the Uganda Bureau of Statistics (UBoS)

as part of the Living Standard Measurement Study-Integrated Surveys of Agriculture (LSMS-ISA)

(4.9)

(4.10)

Essay IV

126

of the World Bank. Among the 3,123 targeted households in 2005/9, the UBoS was able to track

2,888 households in 2009/10, among which only 2,566 had complete information (Ssewanyana and

Kasirye, 2012), which represents an attrition rate of 17, 8%. And among the 2,566 households

tracked in the 2009/10, 2,390 were re-interviewed in 2010/11 and 2,194 in 2011/12, with only 2,173

households having complete information in all the four waves. Hence, for this essay, the final

sample of each survey contains information on 2,173 balanced households79

, located in all the

geographical regions of the country. Pooling these time series and cross-sectional data gives 8,692

observations. All surveys were based on a two-stage stratified random sampling design. In the first

stage, Enumeration Areas80

(EAs) were selected from the 4 geographical regions of the

country and grouped by districts and rural-urban location (UBoS, 2010). In the second stage, ten

households in each EA were selected by simple random sampling. Each household was then visited

twice in order to capture seasonalities in the agricultural production module81

. The panel surveys

provide detailed information on household demographics, production (quantities and values of both

inputs and outputs), consumption (food and non-food commodities), landholdings and livestock

ownership, types of shocks and coping strategies, among others. Different recall periods were used

depending on the nature of the expenditure items: they go from a seven-day recall period for food

consumption to one year for durable, semi-durable and non-consumption expenditures (taxes and

duties, pension, social security contribution, remittances, gifts, contribution to funerals,...).

4.5.1 Construction of a food price shock variable

A key challenge in estimating equation (4.10) is to find a suitable definition of being exposed to a

food price shock. Two practical problems emerge when engaging in such task. First, although the

datasets I are using provide information on households’ exposure to different types of shocks

(health, agricultural, livestock or other asset shocks) as well as the responses in terms of coping

strategies that households adopt, the surveys remain silent in regards to food price shocks, thereby

leaving the researcher to surmise on the likelihood of exposure to price shocks. Second, price

changes affect households differently depending on their tastes, preferences, composition, or their

79

To test for a potential attrition bias, I apply the attrition probits’ tests of Fitzgerald et al. (1998), and the pooling tests of Becketti, Gould, Lillard and Welch (1988). The correction of attrition bias is then done through the inverse probability weighting (IPW) procedure (Fitzgerald et al, 1998; Wooldridge, 2002). See Appendix B.1.

80 An enumeration area represents “the smallest ground area, mapped with definite boundaries within which a study

or interview is carried out” (UBoS, 2012: 32). 81

In the UNPS-2006, households were first visited between May and October 2005 and then between November 2005 and April 2006. In the UNPS-2010, first visits occurred between September 2009 and January 2010 while the second were conducted between February 2010 and August 2010. In the third wave, first visits were conducted between October 2010 and March 2011, while the second were between April and September 2011. For the last survey, first occurred between November 2011 and April 2012 and second between May 2012 and December 2012.


127

decision to participate or not into a food market. Hence, observing a “large” change in food prices

in a specific district between two periods does not automatically imply that all households within

that district will be identically affected. One way to overcome the above complications is “to locate

shocks using a pure statistical definition” (Dehn, 2000: 8). Hence, in order to compute a food price

shock variable, I follow the methodology first developed by Deaton and Miller (1995) and recently

applied by Collier and Dehn (2001) and Combes et al. (2012) in their studies of countries’

vulnerability to commodity price instabilities and shocks.

First, I compute a household-specific consumer price index to reflect households’ heterogeneity in

their consumption preferences. Theoretically, two approaches can be used to obtain these indices.

One could estimate a food demand system and use the estimation results to compute a household-

specific true cost of living (Cage et al., 2002); or instead, one could use a vector of market prices at

a certain disaggregation level (village, district, or sub-region) and a vector of household-specific

budget shares to construct the index. I will use the second approach given its evident computational

simplicity.

Let hctCPI be the food price index, specific to a household h living in cluster (village or district) c

in period t. If ictp represents the median unit market price of a commodity i observed in cluster c at

time t, and

I

i

ihct

ict

ihct

ict

ihct CpCps

1

/ is the food consumption share82

of the commodity i¸ then

hctCPI , based on price levels in period 0 (in this essay, 2005/6), can be computed as a modified

Laspeyres formula:

I

iic

icti

hcthctp

psCPI

1 0

where the basket of goods in equation (4.11) is made up of 7 food commodities or commodity

groups considered as the most important in the Ugandan diet: matooke83

, potatoes (sweet and Irish

potatoes), cassava, maize, beans, meat and fish, fruits and vegetables. Hence, although market

prices are assumed on average identical for households within the same village (Deaton, 1988), the

use of food consumption shares ihcts as individual weights makes the price index household-

specific. Given hctCPI , the second step consists in regressing the changes in each household’s price

index on its lagged values, time dummies t, and household’s fixed effects as follows:

82

I include the imputed values of consumption from self-produced goods 83

Matooke refers to starchy bananas that are cooked and consumed as staple (Haggblade and Dewina, 2010) and represents one of the most important staple foods in the Ugandan diet.

(4.11)

Essay IV

128

TttCPICPI hcthcthct ,...,1;2110

The residuals from equation (4.12), hct , are then standardized by subtracting their mean values

hct and dividing by their standard deviation s (Combes et al., 2012). Hence, contrarily to many

previous studies on shocks, this specification allows not only to answer whether there is a

significant impact of exposure to food price shocks on consumption growth but also how large this

impact is given the magnitude of the shocks experienced by the household. Owing to the emphasis

of the essay on positive price shocks, I consider for now a household as having been exposed to a

food price shock if its normalized residuals from equation (4.12) are positive. This definition will

then be extended thereafter by including negative price shocks and varying cut-off points. The

higher the values of the normalized residuals, the more important the scale of exposure to food price

shocks. Using this definition, there are respectively 63.3, 51.7, and 34.2% households that were

exposed to food price shocks in 2009/10, 2010/11, and 2011/12. The prominence of positive shocks

over 2009-2011 is not surprising since this period corresponds to the recent global food price crisis

but also has seen sharp increases in domestic food prices in Uganda84

.

Table 4.1 presents some key household characteristics according to whether a household was

exposed or not to a food price shock. Households are then subdivided into three categories,

depending on the extent of their exposure to price shocks: high if the normalized hct exceeds the

75th

percentile of the sample value; moderate, if it lies between the median and the 75th

percentile;

and low if it is positive but below the median.

Different features emerge from table 4.1. First, the proportion of highly exposed households is the

largest in 2009/10 (27.6% of surveyed households) and the lowest during the third survey (15.6% in

2010/11). Second, while the number of moderately affected households is decreasing over time,

those of unexposed and with low exposure rates are increasing, reflecting the general tendency of

food price changes in Uganda. Third, we also note that on average households’ monthly real values

of food consumption per adult equivalent were the highest when households were not exposed to

food price shocks. Hence, unexposed households enjoyed an increase in their consumption relative

to those exposed. Among the sub-sample of households exposed to price shocks, those at the

highest vulnerability percentile reported on average a lower level of consumption compared to the

baseline survey (2005/6), providing a first insight on a possible negative relationship between the

degree of exposure to food price shocks and households’ consumption levels.

84

See Essay II.

(4.12)


129

Table 4.1 Household characteristics by exposure to food price shocks

Base

survey:

High

Moderate

Low

None

2005/6 2009/10 2010/11 2011/12 2009/10 2010/11 2011/12 2009/10 2010/11 2011/12 2009/10 2010/11 2011/12

Observations 2173 599 338 492 726 703 101 50 82 150 798 1,050 1,430

Monthly real

food cons.

34,955

(30,359)

32,067

(25,607)

25,056

(17,167)

32,911

(21,703)

33,184

(26,867)

27,875

(22,727)

27,529

(18,524)

33,598

(22,134)

28,885

(23,686)

37,735

(22,802)

34,403

(23,864)

29,443

(21,170)

37,659

(29,893)

Household

size

5.78

(3.03)

6.67

(3.34)

7.49

(3.78)

7.62

(3.68)

6.77

(3.88)

7.45

(3.45)

7.74

(3.63)

6.96

(3.46)

7.80

(3.27)

7.86

(4.85)

6.42

(3.17)

7.01

(3.53)

7.06

(3.93)

Proportion

of children

0.54

(0.23)

0.58

(0.22)

0.57

(0.23)

0.54

(0.22)

0.55

(0.23)

0.55

(0.22)

0.51

(0.22)

0.58

(0.24)

0.54

(0.21)

0.49

(0.23)

0.53

(0.23)

0.54

(0.22)

0.51

(0.22)

Years of

education

5.25

(3.94)

4.73

(3.88)

5.40

(4.15)

5.73

(4.41)

5.11

(4.12)

5.35

(4.26)

4.90

(3.88)

4.38

(3.64)

5.54

(3.97)

8.00

(5.74)

5.39

(4.11)

5.59

(4.29)

5.00

(3.96)

Age of the

head

42.79

(15.00)

47.44

(15.19)

47.74

(15.10)

47.40

(14.89)

46.81

(14.73)

47.58

(15.61)

47.71

(13.06)

43.62

(14.62)

47.96

(15.25)

48.29

(15.53)

46.51

(14.91)

47.00

(15.02)

48.58

(14.76)

% of female-

headed

0.28

0.27

0.24

0.23

0.35

0.38

0.05

0.02

0.03

0.01

0.36

0.35

0.71

% of agr.

households

0.83

0.34

0.26

0.19

0.34

0.38

0.05

0.29

0.05

0.02

0.03

0.31

0.76

% of net

sellers**

0.27

0.28

0.22

0.07

0.35

0.41

0.03

0.03

0.05

0.01

0.34

0.32

0.85

% of net

buyers**

0.55

0.29

0.27

0.26

0.37

0.38

0.06

0.02

0.04

0.02

0.32

0.31

0.66

% of poor

households *

0.28

0.32

0.24

0.18

0.31

0.37

0.04

0.02

0.05

0.01

0.34

0.22

0.78

Note: *

Poor households are defined using the official absolute poverty line of 1 USD PPP per capita/ per day converted into Uganda Shillings (UShs). A household is then

poor if its real consumption (food and non-food) per adult equivalent lies below the poverty line. **

Net sellers (buyers) are defined as agricultural households whose total values

of crop sales are greater (lower) than the total values of consumption of those crops (matooke, cassava, potatoes, maize, beans, rice, millet, sorghum, fruits, and vegetables).

Standard deviations into brackets

130

By and large, the lower the degree of exposure to food price shocks, the more important the

level of consumption. Households likely to be highly exposed to food price shocks have on

average larger household size, higher proportion of children, older heads and are run mostly

by females.

Unsurprisingly, agricultural and poor households display a higher likelihood of being exposed

to large food price shocks. For example, the proportion of agricultural households with low

degree of exposure to price shocks is around 2%, compared to an average of 25% and 26% for

high and moderate degrees, respectively. This feature was expected, particularly for

agricultural households since they generally live in rural areas and dependent essentially on

the levels of market prices for their income. When we disaggregate agricultural households by

their net seller/net buyer status, it appears that globally the proportion of net sellers (buyers)

of food staples is decreasing (increasing) with the degree of exposure. Finally, the fact that

most poor households were highly exposed to price shocks is also in line with many empirical

findings (Cudjoe et al., 2008; Headey and Fan, 2008; Ivanic and Martin, 2008; Boysen, 2009;

Hella et al., 2011) and is indicative of increased risks of being trapped into persistent poverty

for those households.

4.5.2 Asset index

Household wellbeing can be analyzed through different measurement indicators, ranging from

consumption to income and aggregate asset indices. In developing countries, consumption

levels have always been preferred to income due to its potential measurement errors and acute

volatility. Although very informative on household welfare dynamics, consumption-based

approaches fall short of distinguishing structural changes from stochastic variations in welfare

(Barrett et al., 2006). To enrich the analyses from consumption and account for the underlying

structural wellbeing of households, I also compute, in line with Carter and May (2001), Adato

et al. (2006), Carter and Barrett (2006), McKay and Perge (2013), Naschold (2013), and

Kwak and Smith (2014), among others, an aggregate index of household assets. This index

reduces the multivariate dimension of assets to a single dimension, thereby avoiding the

“curse of dimensionality" problem in non-parametric estimations. I use the livelihood-

weighted regression approach (Carter and May, 2001; Adato et al.; 2006; Amare and Waibel,

2013)85

where a livelihood indicator, in this study real monthly values of consumption per

adult equivalent divided by the official poverty line, is regressed over a bundle of assets

85

Another approach to construct an asset index is to use principal components or factor analyses. As indicated by Naschold (2013: 939), “[n]either method of constructing the asset index is inherently superior but one can be a useful validation for the results of the other”.


131

(human, physical, financial, or social) likely to shape household’s wellbeing and the predicted

value of the dependent variable is then used as the estimated asset index. Similar to previous

studies (McKay and Perge, 2013; Naschold, 2013), the components of the asset index include

a set of productive and agricultural assets (land, livestock, agricultural equipments, small

business machinery,…), physical assets (owned houses and buildings, household utilities,…),

and human assets (household size, maximum years of schooling of the head, proportion of

adults and children,…). Formally, this requires estimating the following regression model

(Amare and Waibel, 2013):

hth

I

kj

kht

jhtjk

I

i

ihtiht AAA

ωD'αΖ',1

0

where the dependent variable t

ht

P

c

ht is the real monthly values of consumption per adult

equivalent htc expressed at a percent of the official poverty line86

tP at time t. ihtA ,

jhtA , and

khtA are the amounts of physical or productive assets i,j, and k owned by household h in period

t; Ζ is a vector of households’ characteristics (human assets); D is a vector of district and

time dummies included to account for geographical and time unobserved effects on assets

accumulation, while h stands for household-specific unobserved fixed effects. ht is the

error term. Equation (4.13) is estimated using a fixed-effects model and the predicted values

ht are interpreted as household-specific asset index. Deriving this index through a livelihood

approach presents at least three appealing advantages. First, individual assets are included in

the index based on their marginal contribution on the household’s overall livelihood level.

Second, scaled in Poverty Line Units (PLU), the index is easily interpretable: an index above

1 means that household’s asset holdings would be expected to yield a livelihood level above

the official poverty line. Finally, the asset index can be used to distinguish between stochastic

and structural poverty.

In figure 4.1, I plot the asset index hta at current period against its one period lagged value.

The scatterplot portrays interesting features of households’ assets accumulation. First, there

seems to be an equi-distribution of asset indices below and above the asset poverty line,

particularly between 0.65 and 1.4, with only few observations (gray circles) located outside

this interval. Second, there is evidence of households’ heterogeneity regarding their assets’

accumulation process: households whose asset holdings are below (above) the 45° line will be

decumulating (accumulating) assets over time. Third, and probably the key take-away

86

1 USD PPP per capita/ per day converted into Uganda Shillings (UShs)

(4.13)

Essay IV

132

message from this bivariate analysis, is the evident absence of multiple critical thresholds in

the assets accumulation process: Ugandan households seem to be converging towards a single

asset equilibrium located slightly above the official poverty line.

Figure 4.1 Scatterplot of asset index

4.5.3 Descriptive statistics

Table 4.2 presents summary statistics of key variables used in this study. Household total

consumption expenditures (food and non-food) are fluctuating over time, while household

food consumption expenditures are decreasing. Between the first and second waves, the

average monthly real household expenditures increased by 19.6% to 257,244UShs. Then, they

decreased by 18.9% to 208,727UShs between the second and third rounds, and finally

increased by 23% to 256,640UShs between the third and last rounds. This translated into a

decrease in the proportion of poor between the first two rounds, from 28.1 to 24.8%, an

increase in the number of poor in 2010/11 at 29.1%, and a fall in the last survey at 27.2%.

However, there are little fluctuations in asset indices, which globally increase over time.

Agricultural households, representing more than 80% of the sample, are essentially small-size

farmers, cultivating on average less than 5 acres. In terms of shocks’ occurrences, the majority

of households were exposed to food price shocks in waves 2 and 3 (63.3 and 51.7%,

respectively) against only 34.2% in the last round. Agricultural shocks (droughts, floods, pest


133

attacks and diseases…) were also relatively frequent, with around half of households being

affected in the first three rounds.

Table 4.2 Summary statistics by survey rounds

2005/6 2009/10 2010/11 2011/12

Mean Sd. Mean Sd. Mean Sd. Mean Sd.

Monthly real household

expenditure (UShs)

215,093 379,790 257,244 474,486 208,727 269,133 256,640 534,772

Monthly real food cons. per

adult equiv. (UShs)

34,955 35,359 33,333 25,345 28,560 22,269 28,874 20,377

Asset index (unitless) 1.042 1.247 1.076 1.414 1.067 1.381 1.101 1.282

Land size (acres) 3.261 20.951 2.623 10.444 3.769 23.964 2.397 7.704

Household size 5.758 3.026 6.620 3.265 7.316 3.560 7.946 3.869

Proportion children (%) 0.551 0.231 0.515 0.408 0.521 0.389 0.549 0.383

Education head (years) 5.254 3.936 5.091 4.050 5.451 4.229 5.169 4.083

Age of head (years) 42.786 15.001 46.801 14.928 47.435 14.899 48.268 14.707

Female-headed (%) 0.271 0.287 0.310 0.317

Poor (%)

0.281 0.248 0.291 0.272

Agric. households (%) 0.825 0.845 0.821 0.807

Rural households (%) 0.796 0.799 0.799 0.796

Food price shocks (%) baseline 0.633 0.517 0.342

Agricultural shocks (%) 0.487 0.500 0.484 0.242

Health shocks (%) 0.183 0.113 0.114 0.064

Income shocks (%) 0.108 0.020 0.03 0.087

Other shocks (%) 0.156 0.045 0.050 0.040

Appendix D.1.A plots the distributions of households’ welfare indicators (log consumption

values and asset index) between 2005/6 and 2011/12. The striking feature of these

distributional plots is their shifts to the right in a zigzag fashion, suggesting an overall

improvement in households’ assets accumulation over time coupled with significant

downward and upward movements. These transitions are particularly pronounced with

regards to consumption where for instance the plots of first and third surveys almost entirely

overlap. These trends in asset holdings and consumption expenditures become apparent when

they are expressed in growth rates, as in the second part of Appendix D.1.A which graphs the

density functions of the average annual growth rates of assets and consumption. The median

growth rate of asset index between 2005/6 and 2009/10 was only 3.3% against an impressive

18% in terms of consumption values. However, around 60.5% of households experienced a

positive growth rate in their monthly real values of consumption during that period, whereas

slightly more households (around 61.5%) accumulated assets. Between 2009/10 and 2010/11,

Essay IV

134

the median rates of consumption and assets growth were both negative at respectively -19.8

and -0.8%, with only 37.6% displaying a positive rate of consumption growth and 44.5% for

asset holdings. Finally, both the growth rates of both consumption and asset holdings were

positive during the last sub-period, with a striking 29.3% increase in consumption compared

to 3.2% in assets. 74.1% and 66.6% of surveyed households during this period reported a

positive growth rate of their consumption and asset index.

4.5.4 Poverty dynamics, stochastic, and structural poverty

The analysis of poverty dynamics implies an explicit consideration of time. Indeed, empirical

research on longitudinal data has revealed the importance of movements in and out of poverty

and of the diversity of poverty trajectories from one period to another. Beyond the analysis of

poverty evolutions based on cross-sectional data, it is particularly valuable to identify among

poor households the chronically poor and those who are only transiently deprived. This is of

utmost importance because not only the characteristics of these two types of poverty are not

necessarily identical but also appropriate policy responses to tackle them might be different

(Jalan and Ravallion, 2004; Ribas and Machado, 2007). Using the spells approach (Baulch

and McCulloch, 1998), table 4.3 distinguishes chronically poor, transiently poor, and non-

poor households between 2005 and 2012.

Table 4.3 Percentage of households by poverty dynamics, by region: Spells approach

All sample

Regions

Poverty status Central Eastern Northern Western

Never poor 0.472 0.705 0.375 0.273 0.512

Once poor 0.205 0.148 0.233 0.221 0.235

Twice poor 0.149 0.086 0.208 0.176 0.133

Thrice poor 0.106 0.049 0.124 0.169 0.084

Always poor 0.067 0.013 0.060 0.161 0.036

Using the full sample, around 6.7% of the households were chronically poor between 2005

and 2012, whereas almost half of the sample was never poor (47.2%). The percent of

households into each spell of poverty then decreases with the number of spells, from 20.5%

for once poor to 10.6% for thrice poor. Furthermore, the table sheds some light on regional

heterogeneity in terms of poverty dynamics: households in the central region are particularly

better-off with the highest proportion of non-poor (70.5%) and lowest percent of chronic poor

(1.3%), while the northern and eastern regions display the worst welfare performances.


135

It is also possible to go further into the analysis of poverty dynamics by decomposing

movements into and out of poverty into stochastic and structural transitions using both the

official poverty line and the asset index. Structural movements are related to changes in assets

accumulation while stochastic or transient changes refer to movements in consumption. In

table 4.4, I present a poverty transition matrix between pairs of successive panel waves.

Between two periods t-1 and t, a household will be stochastically poor if its asset index hta is

at least above 1 in both periods while its monthly real values of consumption per adult

equivalent htc lie below the official poverty line tP in both periods. He will be structurally

poor if both 1hta and tht Pc in t-1 and t. A household is downward mobile, meaning he

is falling into poverty if 11 tht Pc , and tht Pc . This mobility will be explained by

stochastic movements if hta 1, t , whereas in case of structural movements, hta 1 and

1hta 1. Similarly, upward mobility implies that 11 tht Pc , and tht Pc . If the household is

climbing out of poverty for stochastic reasons, then both 1hta and hta are greater than 1 and

if this mobility is due to structural factors, then 11 hta , and 1hta . Finally, stochastically

(structurally) non-poor households have tht Pc , t and 1hta , t .

By and large, the results from table 4.4 reveal that between pairs of successive panel waves,

Ugandan households were overwhelmingly non-poor (more than 60% for each pair), while

the shares of those twice poor, downward, and upward mobile were relatively close, ranging

from 10 to 17%. Furthermore, the majority of household transitions into and out of poverty

were attributed to stochastic movements rather than to assets depletion. For instance, over the

first and second survey rounds, only 39.9% of chronic poor experienced a depletion of their

assets while persistent poverty of 60.1% could be attributed to stochastic changes in their

livelihood. The share of households that fell into poverty due to low asset levels during that

period is less than the half of that of stochastically downward mobile. Among non-poor, only

26.4% hold assets that would be expected to yield a livelihood above the poverty line. Hence,

the majority of these non-poor (73.6%) would also be vulnerable in case of shocks of

particularly large magnitude. Between 2009/10 and 2010/11, the proportion of chronic and

downward mobile slightly increases at the expense of other categories. For households that

slid into (out of) poverty during that period, 47.7 (46.1%) were structurally mobile against

43.8 (42.8%) in the previous sub-period. Finally, the table highlights the importance of

structurally persistent poverty over time. Indeed, the proportion of chronically poor

households for structural reasons (reductions in asset holdings) is increasing over time, from

39.9% during the first sub-period to 49.3% in the last sub-period.

Essay IV

136

Table 4.4 Poverty transition matrices

Poor Non-poor

2009/10

2005/6

Poor

Twice poor 13.02 Upward mobile 15.05

Stochastically poor 60.07 Stochastically mobile 57.19

Structurally poor 39.93 Structurally mobile 42.81

Non-

poor

Downward mobile 11.78 Twice non-poor 60.15

Stochastically mobile 56.25 Stochastically non-poor 73.60

Structurally mobile 43.75

Structurally non-poor 26.40

2010/11

2009/10

Poor




Non-

poor



Structurally mobile 47.67 Structurally non-poor 27.82

2011/12

2010/11

Poor




Non-

poor



Structurally mobile 47.01 Structurally non-poor 22.66

4.6 Estimation methods and results

In this section, the key propositions of the study are exposed (4.6.1) and the different

econometric models for analyzing welfare dynamics (consumption growth and assets

accumulation process), identifying critical welfare thresholds, and testing for single against

multiple equilibria are presented (4.6.2 – 4.6.4). Finally, the section highlights the possibility

of shifts in welfare equilibria due to differences in exposure to shocks and regional

heterogeneity (4.6.5) and checks for the robustness of the econometric results by extending

the definition of exposure to food price shocks (4.6.6).

4.6.1 Propositions

Two main propositions are tested regarding the effects of food price shocks on household’s

welfare growth and likelihood of being trapped into poverty. First, I hypothesize that being

exposed to food price shocks is associated with differential welfare growth rates

(consumption and assets accumulation) which signs depend on households’ characteristics


137

and initial conditions. Second, conditional on these characteristics and initial conditions, the

higher the degree of exposure to food price shocks, the higher the likelihood of being trapped

into poverty or converging towards lower levels of welfare equilibria.

Proposition 1: Let 0y , with 000 ,acy and Λ be respectively the initial welfare

level (consumption levels 0c or assets 0a ) and household demographic characteristics.

For two households h and j with identical initial welfare levels (i.e 000, yyy jh )

and household characteristics at time t (net market position, household size, education,

gender of the head, geographical location,…), then the household exposed to food

price shocks will be likely to experience a lower welfare growth (consumption growth

or assets accumulation) at time t+1 than a household who was unexposed. Formally,

this means that:

1,ln1,ln 01,01, fjttj

fhtth yyyy ΛΛ

Proposition 1.1: Given initial welfare levels ( 0c and 0a ) and household h’s

demographic characteristics, the effects of food price shocks will be higher on

consumption growth than on assets accumulation growth:

1,ln1,ln 01,01, f

htthf

htth aacc ΛΛ

Proposition 1.2: Let two households h and j be exposed to food price shocks

at time t+1, with the degree of exposure being higher for h (i.e. 1fjt

fht ).

In this case, conditional on household characteristics and initial welfare levels,

the welfare growth rate between t and t+1 will likely be lower the higher the

degree of exposure to food price shocks. Otherwise stated:

fjttj

fhtth yyyy ,,ln,,ln 01,01, ΛΛ for 1 f

jtf

ht

Proposition 2: Let households h and j with identical initial conditions 0y and

demographic characteristicsΛ . Then the household with a higher degree of exposure

to food price shocks is likely to suffer from a lower welfare equilibrium level.

Formally, if ehy and e

jy are the welfare equilibrium levels towads which households h

and j are converging in the long run, then we have that:

Essay IV

138

fjt

ej

fht

eh yyyy ,,,, 00 ΛΛ if 1

fjt

fht

Figure 4.2 illustrates the above propositions through the hypothetic non-linear welfare

dynamics as theorized by Carter and Barrett (2006). sy represents the welfare subsistence

level (consumption or asset holdings) below which accumulation is deemed impossible. For

simplicity, households’ initial welfare levels ( 0y ) are assumed equal to this survival threshold.

Conditional on their initial welfare levels and demographical characteristics, the households’

accumulation growth path depends on their exposure to food price shocks f

htty 1 .

Figure 4.2 Hypothetic relationships between welfare dynamics and exposure to food price shocks

In this setting, there are three types of welfare equilibria: low stable equilibria 3,2,1, iy eLi ,

high stable equilibria 3,2,1, iy eHi , and unstable equilibria 3,2,1, iy M

i . Prior to any price

shocks, households’ welfare dynamics are given by the 11 f

htty curve, characterized by

low and high stable equilibria eLy 1 and e

Hy 1 .

In case of exposure to food price shocks, households do not necessarily converge towards

their potential welfare equilibria ( eLy 1 and e

Hy 1 ) but there are instead shifts in both their

welfare dynamics and equilibria. For example, the household exposed to price shocks will

eHy 2

eHy 2

eHy 3 My3 My2 My1 e

Hy 1 ty

)1(1 f

htty )1(1

fht

fjtty

0yys eL

y3 e

Ly 2 eL

y1

eL

y3

)1(1 f

htty

line45 1ty

eLy 2 eL

y3

eL

y1

My1

My2

My3

eHy 3

eHy 2

eHy 1


139

follow a dynamic path (blue curve) located below that of an unexposed household and he will

thus converge to much lower stable equilibria eL

eL yy 12 and e

HeH yy 12 . Hence, given initial

welfare levels and demographic characteristics, exposure to food price shocks leads to lower

welfare growth path 11 f

htty . When it comes to comparison of two households exposed to

food price shocks, the one with a higher degree of exposure will be characterized by lower

welfare equilibria: eL

eL

eL yyy 123 and e

HeH

eH yyy 123 .

4.6.2 Parametric models of consumption and asset dynamics

The starting point of our estimation strategy is given by equation (4.10). In line with existing

studies (Jalan and Ravallion, 2002; Barrett et al., 2006; Kwak and Smith, 2010; Naschold,

2013), I allow for nonlinearities in welfare dynamics by estimating changes in consumption

htcln as a cubic polynomial function of lagged consumption 1htc , household characteristics

Λ , and changes in exposure to food price shocks f

htln and other asset shocks k

t . Hence,

our baseline empirical model is given by:

hthj

kj

tj

f

ht

i

htii

ht cc

3

111

3

10 lnlnln αΛ'

where the dependent variable htc represents monthly real values of consumption per adult

equivalent in period t; Λ denotes a set of household characteristics, some of which are time-

varying and others time-invariant, likely to influence household consumption levels.

Specifically, I include in Λ household size )(hsize , dependency ratio )(dratio , age of the

head )(age , age squared )2(age , gender )(sex , tropical livestock units )(tlu87

, years of

education of the head )(educ , land size in acres ( )land , household’s poverty status (

povstatus ) as well as regional ( region ) and time ( )year dummies to control for geographic

and time effects, respectively. i are the coefficients of consumption polynomial terms; h is

the time-invariant component of the error term indicating household’s unobserved effects,

potentially correlated with Λ but not with ht ; ht is an independent and identically

distributed (iid) error term; and the remaining right-hand side variables have been previously

defined. Capital/asset shocks are subdivided into three categories: health shocks (1k

ht ) which

87

The concept of Tropical Livestock Unit (TLU) represents a way of quantifying and aggregating a wide range of different types of livestock types/sizes into a single number by applying different exchange ratios among species. In this study, I used: 1 TLU = Camels 1.0; Cattle 0.7; Sheep/Goats: 0.1.

(4.14)

Essay IV

140

take 1 if in the last 12 months a household member died, had severe injury or accident, had a

serious illness, or if the household experienced the death of a member or close relative for

whom it had to pay for the burial. Agricultural shocks (2k

ht ) equal 1 if the household

experienced in the last 12 months droughts, floods, or pest attacks and diseases, causing

output losses, or faced increases costs of agricultural inputs and theft of agricultural assets.

Income shocks (3k

ht ) take 1 if in the last 12 months a household member lost a job or faced

reduction of earnings.

In this baseline specification, food price shocks enter linearly the empirical dynamic welfare

equation (4.14) which would suggest a homogeneous impact of price shocks. I extend this

model by investigating the presence of nonlinear effects of food price shocks on consumption

growth in the following way. I assume that the impact of food price shocks will be different

depending on the degree of a household’s vulnerability to price shocks. Adapting the criteria

of countries’ vulnerability to commodity price instabilities as advanced by de Janvry and

Sadoulet (2008) and applied by Combes et al. (2012), I identify three factors that might

determine this vulnerability. The first factor, food dependency, is related to the importance of

food consumption in the household’s budget. At a given period t¸ a household will be hit by

food price instabilities the larger the share of food consumption in his budget. This degree of

food dependency is approximated by the share of the total value of food consumption in the

household’s total expenditures. The second factor concerns the extent of market participation

in household consumption. Households that rely mainly on home production for consumption

needs will be marginally affected than those constrained to purchase a large proportion of

their food consumption, such as non-agricultural households or significant net buyers. Hence,

the higher the degree of market participation, the higher the likelihood of being exposed to

food price shocks. This second criterion is measured by the ratio of total food purchased to

total food consumption. Finally, food price shocks may have differential impact on

households depending on whether they are rich or poor. Indeed, it has been shown that poor

households are generally more vulnerable to shocks and lack sufficient resources to play as

safety nets in case of shocks’ occurrence (Dercon and Krishnan, 2000; De Weerdt, 2004;

Santos and Barrett, 2006). I measure this ability of households to mitigate the effects of price

shocks by the level of monthly real income per adult equivalent. These three factors are then

combined to compute a household’s vulnerability index to food price shocks ( htvul ) using the

principal component analysis. The higher the value of the index, the more vulnerable the


141

household to food price shocks. The variable of price shocks fht is finally interacted with the

vulnerability index as follows:

htj

kj

tjhtht

f

ht

f

hti

i

htiht

vulvul

cc

3

132

1

3

110

ln

lnlnln αΛ'

where hthht

This specification allows the impact of food price shocks to differ between households given

their degree of vulnerability to price shocks. The coefficient 1 captures the impact of price

shocks due to the actual level of exposure while 3 provides the impact related to the

household’s predisposition to being vulnerable to price shocks. In addition, equation (4.15)

can also be used to test both nonlinearities in price effects and our propositions 1 (and its

corollaries) and 2. The total effect of changes in exposure to food price shocks on

consumption growth rate is thus given by

h

cluv

fht

ht21

ln

lnˆˆ

, where 1 and 2 are the

estimated coefficients and ht

T

tTh vulluv

1

1 is the household’s h average vulnerability index

over the sample period. Hence, checking for nonlinearity simply implies testing the null

hypothesis that 2 is statistically different from 0. The proposition that food price shocks

have detrimental consequences on consumption growth is akin to having 0ˆˆ 21 hluv .

Finally, when 1 and 2 display opposite signs, it is possible to derive a threshold

vulnerability index 2

1ˆ

ˆ

hvul above which food price shocks start hurting households

(reducing their consumption growth).

The dynamic consumption growth model in (4.15) can equivalently be written in levels as:

ht

j

kjtjhtht

fht

fht

i

ihtiht

vulvul

cc

3

1

32

1

3

1

10

ln

lnlnln αΛ'

The estimation of these non-linear dynamic panel models poses some practical problems.

First, the construction of our food price shock variable suggests that f

ht will be endogenously

determined since it is correlated with household characteristicsΛ . To solve this problem, one

could use an instrumental variables’ estimation (such as Two Stage Least Squares, 2SLS).

(4.16)

(4.15)

Essay IV

142

However, with weak instruments, the fixed-effects IV estimators will be biased. Second, it is

well known that OLS will yield inconsistent estimates since the polynomial terms in

consumption 3,...,1,1

ic i

ht will be correlated with the error term hth . As a result, the

coefficients i will be inflated upwardly (Hsiao, 1986; Bond, 2002), leading again to

potential endogeneity problems and estimation instability. A possible way-out to reduce this

upward panel bias is through a within-groups (fixed effects) transformation that wipes out

household-specific time-invariant effects h . However, given the structure of our panel dataset

(small T, large N), this solution is also unsatisfactory as it has a tendency towards downward

panel bias (Nickell, 1981). The panel bias will be captured by introducing the first difference,

which purges the fixed effects h . To estimate the consumption growth model, I use the

System Generalized Methods of Moments (S-GMM) of Arellano-Bover (1995) and Blundell-

Bond (1998). Indeed, the S-GMM reduces the problem of finite sample biases associated

with weak instruments and estimates a system of equations both in first differences and in

levels. Blundell and Bond (1998) suggest that lagged levels of the variables are suitable

instruments in the difference equation, whereas in the levels equation, lagged differences are

used as appropriate instruments. The implementation of S-GMM depends on the satisfaction

of serial correlation and over-identification tests. The Sargan/Hansen test checks whether the

set of instruments as a group are properly identified and valid. Therefore, the higher the p-

value of this statistic, the better88

. The Arellano-Bond test for autocorrelation AR(2) detects

autocorrelation in levels and failure to pass test implies that the S-GMM estimator is

inconsistent.

Table 4.5 reports the two-step S-GMM estimation results of consumption growth model using

four different specifications. Model I leaves aside shock variables (food price, health,

agricultural, and income shocks) and regional and time dummies. Model II extends Model I

by allowing for location and time dummies; the third specification takes account of both

different shock variables and regional and time effects but only assumes linear effects of food

price shocks. The last specification (Model IV) allows for potential nonlinear effects of price

shocks. Specification tests were performed using both serial correlation and over-

identification tests.

88

The choice between the Sargan and Hansen tests depends on whether the robust option is used, the Hansen test being applied in robust estimations.


143

Table 4.5 Two-step system GMM estimation of consumption growth model

Dependent variable: htcln

Model I Model II Model III Model IV

Polynomial terms

1htc -1.268 (0.009)

*** -2.395 (0.315)

*** -2.972 (0.084)

*** -2.795 (0.087)

***

21htc

0.562 (0.455) 0.315 (0.022)***

0.256 (0.077)***

0.765 (0.264)***

31htc

-0.056 (0.049) -0.075 (0.024)***

-0.074 (0.025)***

-0.025 (0.009)***


hsize 0.015 (0.001)***

0.071 (0.007)***

0.063 (0.006)***

0.039 (0.007)***

dratio 0.032 (0.017)*

0.131 (0.064)***

0.129 (0.059)**

0.313 (0.77)***

age 0.025 (0.062) 0.142 (0.038)***

0.099 (0.031)***

0.050 (0.030)*

2age -0.002 (0.006) -0.001 (0.004)

*** -0.001 (0.000)

*** -0.000 (0.000)

*

sex -0.010 (0.040) -0.085 (0.028)***

-0.082 (0.028)***

-0.041 (0.023)*

tlu -0.007 (0.002)***

0.008 (0.002)***

0.008 (0.003)***

0.001 (0.001)

educ 0.042 (0.019)**

0.020 (0.002)***

0.019 (0.004)***

0.000 (0.003)

land 0.005 (0.021) 0.052 (0.014)***

0.056 (0.001)***

0.021 (0.013)*

Sensitivity to food price and asset shocks

fht

-0.183 (0.079)**

-0.775 (0.239)***

fht

htvul

0.568 (0.225)

**

htvul -0.207 (0.094)

**

1kht

-0.047 (0.021)**

-0.010 (0.018)

2kht

-0.106 (0.031)

*** -0.040 (0.019)

**

3kht

-0.045 (0.005)***

-0.096 (0.056)*

povstatus

-0.572 (0.245)***

region No Yes Yes Yes year No Yes Yes Yes

Specification tests )1(AR 0.016

** 0.093

*** 0.000

*** 0.000

***

)2(AR 0.147 0.175 0.661 0.378

Hansen J 0.386 0.935 0.156 0.725

Joint significance test: 0ˆ1 and

0ˆ2 , p-value

0.002

Vulnerability threshold: hvul

1.364

Percent of households above

hvul by survey (

a)

57,65 (69.61;

62.80; 40.53)

Note: (a) The percents of households above the vulnerability threshold are related to the surveys 2009/10,

2010/11, and 2011/12. The average percent throughout the sample is first reported and then disaggregated by

survey round (into brackets). Robust standard errors into brackets. . ***

, **

, and * denote statistical significance at

10, 5, and 1% levels, respectively.

Essay IV

144

In all the four models, the null hypothesis of the Arellano-Bond test of autocorrelation in first

differences AR(1) is rejected while the test of AR(2) indicates that the S-GMM estimators are

consistent in all models. The Hansen J statistic concludes that our instrumental variables, as a

group, are valid.

The effects of the polynomial terms on households’ consumption growth reveal some

interesting features. First, the results show that the coefficients of one-period lagged

consumption expenditures affect households’ consumption growth negatively and

significantly in all model specifications, which indicates that households’ consumption

growth between periods t-1 and t tend to decrease the higher the levels of consumption in t-1.

Particularly, these estimated coefficients exceed one in all specifications and are the lowest

when regional and time dummies are excluded from the consumption growth model. Second,

the quadratic and cubic polynomial terms are respectively positive and negative in all models

but simultaneously insignificant only in Model I, which implies a linear consumption growth

path. In the other models, the hypothesis of nonlinearities in the growth rate of consumption is

not rejected at 5% significant level in the richer specifications.

All shock variables are both negative and significant at 5% levels. Particularly, the results

confirm our proposition 1 that being exposed to food price shocks lowers the rate of

consumption growth. In model III, the coefficient 1 associated with food price shocks is -

0.18%, thereby indicating that a 1% increase in the growth rate of food price shocks is

followed on average by a 0.18% decrease in consumption growth.

The last column of table 4.5 (Model IV) reveals that allowing for nonlinear effects of the

impact of food price shocks modifies considerably the estimation results. Indeed, the p-value

of the joint significance test of 1 and 2 rejects the hypothesis of linearities of price shocks.

Hence, once we allow for the presence of these nonlinear effects, the coefficient 1 becomes

amplified to -0.78 while the coefficient 2 for the interaction between price shocks and the

vulnerability index is positive and significant at 5%. These results suggest that the

consumption growth rate is on average marginally decreasing with the degree of exposure to

food price shocks, and this effect is increasing with the extent of household’s vulnerability.

The higher the vulnerability index, the lower the growth rate of consumption once a

household is hit by a food price shock. The destabilizing effect of food price shocks is

consequently reinforced by higher food dependency, higher degree of market participation,

and lower income levels. However, being potentially vulnerable to food price shocks does not


145

necessarily imply that a household will be negatively affected if the price shock effectively

occurs. In the lower part of table 4.5, I thus report the level of vulnerability index above

which exposure to food price shocks has detrimental effect on consumption growth rate.

Given the estimated coefficients 1 and 2 , the threshold vulnerability index hvul is set at

1.36489

, which means that the consumption levels of households reporting a vulnerability

index above that threshold would be negatively affected in case of exposure to food price

shocks. The percent of households beyond this critical vulnerability level is given in the last

line of table 4.5. Hence, the majority of households should have been particularly concerned

by food price shocks because around 57.7% of surveyed households had a vulnerability index

greater than 1.364. Over time, this percent has been however decreasing, from 69.6% in

2009/10 to 40.3% in 2011/12.

To see whether households located below and above this threshold are intrinsically different,

Appendix D.2 summarizes some key statistics of these two groups of households. In line with

our priors, households above the vulnerability threshold reported on average 24% higher food

dependency, 18.8% higher market participation rate, and 80.1% lower per capita income than

those below hvul . The last column of the appendix also reveals that these mean differences

were statistically significant at 1% level. Furthermore, higher vulnerability appears to be

negatively correlated with the education of the head insofar as highly vulnerable households

are ruled by on average by less educated heads. Finally, I do not find any statistically

significant difference between these two groups of households as of the household size.

In terms of asset/income shocks, being exposed to health shocks (1k

ht ) has a negligible effect,

while the occurrence of agricultural (2k

ht ) and income shocks (3k

ht ) reduces consumption

growth in Model IV by 0.04 and 10%, respectively.

Many household-level variables have also contributed significantly to the consumption

growth rates and present the expected signs. I find life-cycle effects in consumption growth: it

tends to increase with age but only up a certain point before eventually declining. Similarly to

Jalan and Ravallion (2002), the estimation results reveal that larger households tend to have

higher consumption growth rates. Moreover, there are significant gender differences insofar

as female-headed households are likely to have lower growth rates of consumption

expenditures. Moreover, I find evidence that households with more TLUs, larger dependency

89

Alternatively, one could derive this threshold level through a dynamic panel threshold model using non-linear System-GMM as implemented by Masten et al (2008), Chami et al (2009) or Combes and Ebeke (2012).

Essay IV

146

ratio, and more educated heads, displayed higher growth rates, whereas poor households have

significantly lower subsequent rates of consumption growth.

Finally, as expected, increases in land holdings are translated into increases in growth rates of

consumption. This result perfectly characterizes the Ugandan economy where the majority of

households are not only engaged in agricultural activities but also use the products of their

farm for subsistence consumption. Therefore, more lands to cultivate imply more food for

home consumption. And given that food consumption often represents the largest share of

household’s total expenditures, this situation ultimately leads to an increase in consumption

growth rates.

The above analyses of changes in growth rates of consumption give first insights on

household welfare dynamics in Uganda. However, as pointed out by Barrett et al. (2006),

restricting the analysis to consumption prevents us from identifying structural and stochastic

patterns of welfare dynamics and distinguishing the characteristics of one from another.

Hence, to focus on the structural part of household’s welfare, they suggest instead the study of

asset dynamics, less likely to be sensitive to transitory variations. These dynamics may be

determined by both household accumulation behavior and various asset shocks. Similarly to

the above consumption growth model, the assets accumulation process can be described

through a cubic polynomial regression model as follows:

hthkth

kt

fht

i

ihtiht

apovstatusa

aa

70,65

4

3

1

10 lnlnln ΛγΛ'

where kt is a composite asset shock constructed by summing health (

1kht ), agricultural (

2kht ), income (

3kht ), and other asset shocks ( )4k

ht . It thus ranges from 0 (household did not

face any type of asset shocks in the last 12 months) to 4 (household experienced each asset

shock). Accordingly, asset shocks are incorporated linearly into the assets accumulation

growth equation (4.17). They are also interacted with household asset poverty status

apovstatus (which takes 1 if household asset index is below 1 and 0 otherwise) to allow for

heterogeneous patterns in the effects of asset shocks across households. 0,ha stands for

household’s initial asset index.

Table 4.6 displays the estimation results of equation (4.17) using a two-step S-GMM

regression of Arellano-Bover (1995) and Blundell-Bond (1998). All model results reveal that

(4.17)


147

the coefficients associated with the first and cubic polynomial terms are negative whereas the

quadratic term is significantly negative, which implies, similarly to the consumption growth

model, nonlinearities in growth rates of assets accumulation. In the richer model (III), all

selected household characteristics significantly affect the growth rate of assets accumulation

which tends to increase with household size, the age of the household head – but up to a

certain age -, the years of education, and decrease with initial asset holdings or when

households are female-headed or have a high dependency ratio.

Table 4.6 Two-step system GMM estimation of asset index growth model

Dependent variable: htaln

Model I Model II Model III

Polynomial terms

1hta -0.711 (0.074)

*** -0.715 (0.067)

*** -0.984 (0.190)

***

21hta

0.155 (0.106) 0.135 (0.115) 0.235 (0.119)**

31hta

-0.029 (0.016)**

-0.026 (0.017) -0.035 (0.016)**


hsize 0.028 (0.007)***

0.022 (0.008)***

0.034 (0.007)***

dratio -0.093 (0.030)***

-0.084 (0.023)***

-0.279 (0.113)**

age 0.103 (0.058)*

0.057 (0.067) 0.179 (0.060)***

2age -0.001 (0.000)

* -0.001 (0.001) -0.002 (0.001)

***

sex -0.042 (0.022)*

-0.025 (0.025) -0.072 (0.022)***

educ 0.032 (0.003)***

0.028 (0.003)***

0.034 (0.004)***

0,ha -0.247 (0.125)*

Sensitivity to food price and asset shocks

fht

-0.014 (0.002)**

1&0 apovstatuskt -0.102 (0.015)

***

0&1 apovstatuskt -0.009 (0.017)

1&1 apovstatuskt -0.152 (0.014)

***

0&2 apovstatuskt -0.024 (0.021)

1&2 apovstatuskt -0.157 (0.024)

***

0&3 apovstatuskt -0.074 (0.023)

***

1&3 apovstatuskt -0.177 (0.028)

***

region No Yes Yes year No Yes Yes

)1(AR 0.005***

0.008***

0.008***

)2(AR 0.125 0.312 0.344

Hansen 0.118 0.509 0.411

Observations 6,519 6519 6519

Note: Robust standard errors in brackets. ***

, **

, and * denote statistical significance at 10, 5, and 1% levels,

respectively.

Essay IV

148

In terms of the impact of shocks on assets accumulation growth, the results suggest that,

although being exposed to food price shocks significantly reduce the assets growth rates, their

impact appears relatively marginal compared to changes in consumption growth rates. Indeed,

a 10% increase in the degree of exposure to a food price shock would be expected to decrease

the assets growth rate by only 0.14%, largely lower than the 2.07%90

fall in consumption

growth rates. This validates our sub-proposition 1.1 that the marginal effects of changes in

food price shocks’ exposure are much more important on consumption growth than on assets

accumulation. Moreover, the results show that the effects of asset shocks are much more

important than those of food price shocks. However, these impacts appear nonlinear across

asset poverty status and the number of asset shocks faced by the households. Households who

are structurally poor are found not only more sensitive to the occurrence of asset shocks but

also their sensitivity increases with the number of asset shocks. The results reveal for example

that the growth rates of assets accumulation of structurally poor households fell on average by

0.15, 0.16, and 0.18% when they faced one, two, and three types of asset shocks, respectively.

Despite being also sensitive to shocks, assets accumulation rates of structurally non-poor

households are only marginally affected. As pointed out by Amare and Waibel (2013), these

households are generally engaged in high-return livelihood activities which increase their

resilience to different shocks. Indeed, the growth rate of their assets will shrink by only

0.07% in case of exposure to three types of asset shocks against 0.18% for structurally poor.

These results outline the inability of structurally poor households to maintain the welfare

levels in the wake of shocks and other stressors and therefore shed light on the increased

likelihood of being trapped into poverty or converging towards low level welfare equilibria.

Testing for poverty traps

The results of the parametric models of consumption growth and assets accumulation process

have revealed the existence of nonlinearities in household welfare dynamics. However,

finding these nonlinearities does not necessarily imply the presence of poverty traps or

guarantee welfare multiplia equilibria (Kwak and Smith, 2010). To test for the existence of

poverty traps, I first predict the values of consumption expenditures and asset indices using

the estimation results presented in tables 4.5 and 4.6. I add to these results the lagged values

of consumption 1htc and asset 1hta to get the predicted consumption levels and asset index.

The relationship between these predicted values against their lagged values are then portrayed

90

The sum of 1 and 2 in model IV


149

graphically through a scatterplot. If there are multiple welfare dynamic equilibria, then we

must find an S-shaped curve or non-convex welfare dynamics characterized by the existence

of multiple stable equilibria (with at least one equilibrium below the poverty line) and at least

one unstable dynamic equilibrium (Barrett and Carter, 2013).

Figure 4.3 shows markedly linear welfare dynamics with the absence of any S-shaped curve

or bifurcated welfare dynamics necessary for the existence of multiple critical thresholds.

Figure 4.3 Consumption and asset dynamics: Predicted values using parametric methods

On the contrary, the 45 degree line cuts both consumption and asset dynamics’ lines at one

point, suggesting a single dynamic welfare equilibrium at around 29,000UShs for monthly

real values of consumption per adult equivalent and 1.10 PLUs for asset index. These

equilibria are at relatively low level, slightly above the poverty line of 23,760UShs91

for per

capita real monthly consumption.

91

This value represents the average of poverty lines for each survey round.

Essay IV

150

Testing for conditional convergence

The evidence of a single welfare equilibrium in either consumption values or assets

accumulation suggests that households above that threshold are expected to converge

downwards until they reach the stable equilibrium whereas those below the threshold will

eventually improve their welfare levels and approach upwards the stable equilibrium. A

standard empirical question is thus whether there is conditional convergence in the welfare

data and, particularly, whether the convergence is occurring within or between villages or

districts at identical speeds. Following Dercon (2004), I test parametrically these questions by

estimating the following model:

htkht

fht

dht

dhththt yyyy 43121110 lnlnlnlnln ΛγΛ'

where the dependent variable is the growth rate of either consumption or asset holdings. dhty 1

stands for the average welfare level in village/district d in period t-1. All the other variables

were defined previously.

The conditional convergence at the district level implies a negative and significant coefficient

1 , while the hypothesis of convergence at different speeds can be tested using a Wald test of

21 . Table 4.7 presents both the estimated results of equation (4.18) using a two-step

GMM regression and the conditional convergence tests for consumption and assets.

Table 4.7 Conditional convergence tests of welfare dynamics: Two-step GMM estimation

Dependent variable:

ht

cln htaln

0 0.855 (0.084)***

-0.007 (0.021)

1 -0.912 (0.025)***

-0.668 (0.030)***

2 -0.531 (0.078)***

-0.464 (0.071)***

3 -0.209 (0.019)***

-0.032 (0.018)*

4 -0.021 (0.010)**

-0.059 (0.031)*

Λ Included Included

Convergence test

Test: 21 (p-value)

0.000***

0.004***

Observations 6,519 6,519

Note: Robust standard errors in brackets. ***

, **

, and * denote statistical significance at 10, 5, and 1% levels,

respectively.

(4.18)


151

The estimated coefficients 1 are statistically significant and negative, shedding light on the

convergence process within Ugandan districts in terms of consumption and assets

accumulation. Similarly to Dercon (2004) in the Ethiopian case, these results suggest that

richer districts are enjoying higher growth rates of consumption and assets accumulation (

12 ) than poorer districts. Furthermore, the Wald tests reject the null hypothesis that

convergence across districts are occurring at identical speeds. Since 1 is significantly larger,

in absolute terms, than ,2 welfare convergence speeds are significantly different across

districts than within the same districts.

4.6.3 Non-parametric models of consumption and asset dynamics

One of the main drawbacks of parametric methods developed above is that they require the

researcher to specify pre-determined functional forms for the welfare dynamics process.

Contrary to parametric methods, the appeal of non-parametric approach stems from letting the

data determine the appropriate model specification without imposing any parametric

assumptions on the data generating process. The functional form to be estimated is then

unknown by the researcher and can be expressed as:

hthththththt acyyfy ,,1

with ~ TtandNhN 2,1,;0 2

The non-parametric bivariate relationship between the current welfare level hty and its lagged

values portrayed in equation (4.19) can be estimated using various non-parametric methods

such as Kernel-weighted local polynomial smoothing, locally weighted scatterplot smoother

(LOWESS), or different types of splines. In figures 4.4 and 4.5, I only present the results of

consumption (figure 4.4) and asset (figure 4.5) dynamics using location polynomial

smoothing and LOWESS estimates. Other non-parametric techniques, such as splines,

provided substantially identical welfare recursion diagrams and are thus omitted for brevity.

For each welfare indicator, I first report the LOWESS estimates and then the local polynomial

smoothing diagrams (using an Epanechnikov kernel function with 3 degrees). The dashed

lines stand for the 45 degree line and helps locate welfare threshold equilibria. Moreover, the

range of the consumption graphs has been truncated at the 99th

percentile under the

assumption that all extreme values are either outliers or due to measurement errors. Two

features emerge from these non-parametric estimations. First, while consumption and asset

dynamics paths are not exactly linear, they do not exhibit a typical S-shaped curves

hypothesized by the theory of poverty traps (Carter and Barrett, 2006).

(4.19)

Essay IV

152

Figure 4.4 Consumption dynamics: LOWESS estimates and Kernel-weighted local polynomial smooth

Figure 4.5 Asset dynamics: LOWESS estimates and Kernel-weighted local polynomial smooth

Similarly to parametric methods, there is evidence of a single welfare dynamic equilibrium

characterizing consumption expenditures and assets accumulation paths in Uganda. The 45°

lines cross the consumption and assets curves at around 31,000UShs and 1.07 PLUs,

respectively, slightly above the poverty lines. Second, as of the LOWESS curves, although


153

the observations appear widely distributed, consumption and asset plots do not show any

substantial division of observations (represented by gray circles) into distinct subgroups with

heterogeneous welfare characteristics, contrarily to the theory of bifurcated welfare dynamics

of Carter and Barrett. Conversely, household asset holdings and consumption growth are

distributed along the LOWESS curves, with some evidence of clustering of observations

below 60,000UShs threshold for consumption.

4.6.4 Semi-parametric methods

Semi-parametric methods include both parametric components (such as time dummies and

other explanatory variables), and a non-parametric component 1htyf , with

., 111 hththt acy By incorporating control variables and allowing the data to dictate the

shape of the relationship between current welfare indicators and their previous values, semi-

parametric methods gain in precision and robustness (Libois and Verardi, 2013). They often

avoid unobserved heterogeneity problems arising from excluding control variables in non-

parametric techniques (Naschold, 2013). They are often referred to as partially linear models

with the following general specification:

hthhtht yfy 1βXht

where h is the household h’s random or fixed effects and X is a vector of household

characteristics such as age, gender, household size, and education. I run the Ruppert and al’s

(2003) semi-parametric penalized splines estimator92

. The semi-parametric estimations of the

relationship between the current welfare levels (consumption levels and asset indices) and

their lagged values using the Ruppert and al.’s (2003) estimator are displayed in figure 4.6.

What is evident from these figures is that despite nonlinearities in both consumption

expenditures and assets accumulation, the recursion diagrams are in line with the results from

(non-) parametric methods: they reveal the absence of multiple dynamic equilibria

characterizing households’ welfare paths. They show instead that households are converging

towards a single welfare equilibrium located approximately at 31,500UShs for monthly

consumption and 1.13 PLUs for asset index.

92

Other semi-parametric estimators include Baltagi and Li’s (2002) semi-parametric fixed effects estimator, Yatchew’s difference estimator, or Robinson’s double residual estimator.

(4.20)

Essay IV

154

Figure 4.6 Semi-parametric penalized spline regression estimation: Consumption and asset

dynamics

4.6.5 Shifts in welfare equilibria, exposure to food price shocks, and regional

heterogeneity

So far, the estimation results relied on the assumption that all the sampled households share

fundamentally similar dynamic welfare accumulation paths. However, different factors may

lead households to display significantly different welfare trajectories or converge towards

different welfare equilibria. For example, table 4.3 has revealed that the poverty profile of

Ugandan households is not uniformly distributed across the country, some regions being

particularly more vulnerable than others. As highlighted by Jalan and Ravallion (2002)

through the concept of geographical poverty traps, regional heterogeneity in terms of access

to certain facilities (roads, transportation means, health structures,…) may be a powerful tool

in explaining heterogeneous welfare dynamics within a country. Furthermore, high exposure

to food price shocks may also undermine households’ efforts to climb out of poverty or

increase their likelihood of falling into poverty (Ivanic and Martin, 2008), and therefore

ensnare them at lower welfare equilibria. The net seller/net buyer status may also discriminate

households regarding their welfare equilibria, while households below and above the

vulnerability threshold might converge towards different equilibria.

To assess the possibility of heterogeneous welfare dynamics and shifts in equilibria

consecutive to differentials in the degrees of exposure and vulnerability to food price shocks,

regional heterogeneity, and other households’ observed characteristics, I locate welfare


155

equilibria from different econometric methods when households are grouped into categories

sharing similar features. Graphically, the shapes of welfare recursion diagrams were globally

similar to those of the full sample inasmuch as they display single dynamic equilibria.

However, they do differ in the location of those equilibria. Tables 4.8 and 4.9 report the

estimated approximate locations of welfare dynamic equilibria by sub-groups of population.

In terms of consumption, table 4.8 reveals that sub-groups of the Ugandan population are

moving towards different welfare thresholds, regardless of the specified econometric method.

Table 4.8 Approximate locations of real consumption equilibria by estimation methods

Non-parametric methods Cubic

parametric

regression

(S-GMM)

Ruppert et

al.’s

penalized

splines

LOWESS Kernel linear

Polynomial

regression

Kernel cubic

polynomial

regression

Mean Mean CI Mean CI Mean Mean

All sample 30,000 31,000 [28,000;32,500] 30,500 [29,000;32,000] 29,000 31,500

Male-headed households 30,000 32,000 [28,700;33,500] 31,000 [29,500;32,000] 29,900 31,600

Female-headed hhds 29,000 30,000 [27,300;31,600] 29,800 [27,200;30,400] 28,000 31,200

Head with no educ. 25,000 23,000 [20,500;26,200] 25,000 [23,800;26,500] 27,000 29,300

Head with primary educ. 29,000 29,000 [26,500;33,600] 28,800 [27,000;29,200] 30,000 31,100

Head with sec. educ. 37,000 38,000 [35,300;41,100] 36,900 [31,000;38,500] 34,500 33,600

Head with higher educ. 42,500 42,500 [33,500;47,800] 43,000 [38,500;50,000] 32,000 35,200

Agric. Households 28,000 29,000 [25,000;33,000] 29,800 [26,700;31,500] 29,800 30,800

Net sellers 28,000 31,200 [24,100;34,800] 33,000 [27,000;34,000] 28,000 28,000

Net buyers 29,000 28,000 [26,500;32,700] 28,900 [24,000;30,000] 30,000 29,000

Non-agric. households 42,500 33,000 [28,000;38,000] 37,000 [30,000;40,000] 36,000 34,900

Poor households 24,000 24,000 [20,100;32,700] 24,200 [21,000;25,000] 20,000 28,200

Non-poor households 36,500 33,800 [29,000;36,000] 35,000 [30,000;37,200] 37,500 32,700

Exposed to price shocks 30,000 29,000 [24,000;36,800] 30,000 [26,000;34,200] 30,500 31,800

High exposure 28,300 27,000 [24,400;30,000] 28,500 [26,500;33,000] 28,000 29,800

Moderate exposure 30,000 31,000 [25,200;33,000] 31,200 [26,000;36,000] 31,000 30,800

Low exposure 31,500 33,000 [29,000;37,000] 33,500 [28,300;35,000] 32,000 32,900

Unexposed to price shocks 32,000 32,600 [26,500;36,000] 32,000 [28,000;36,500] 32,000 33,200

Above the vulnerability threshold 21,000 22,000 [17,000;21,000] 20,000 [18,000;22,000] 21,000 23,000

Below the vulnerability threshold 34,000 34,000 [30,000;37,000] 34,100 [32,000;36,000] 34,000 32,000

Central region 36,000 37,000 [31,000;40,200] 35,000 [33,500;38,500] 35,000 34,100

Eastern region 27,500 28,000 [25,200;35,800] 28,200 [25,000;29,000] 28,000 31,000

Northern region 27,200 26,000 [20,000;31,300] 25,700 [24,000;26,700] 27,800 29,200

Western region 30,000 28,500 [25,000;31,000] 29,000 [27,000;32,000] 30,000 31,300

Note: Extreme or outlier household expenditures were defined as those beyond the 99th

percentile and replaced

by values observed at that percentile. CI stands for confidence intervals.

Essay IV

156

For instance, male-headed households are expected to converge to higher consumption levels

than their female counterparts. On average, their dynamic welfare equilibrium is 4.4%93

higher than what female-headed households could reach. Education of the household head is

also positively correlated with the welfare equilibrium: the higher the level of education

attained by the household head, the higher the dynamic equilibrium he is expected to reach in

the long run. Particularly, everything held constant, non-educated heads are found to converge

consistently to lower welfare equilibria. Heads with university education are expected to settle

at an equilibrium that is on average 8.44, 31.98, and 50.97% higher than that of non-educated

and heads with primary and secondary education, respectively.

Moreover, differences between agricultural and non-agricultural households, on the one hand,

and on the other, poor and non-poor households, is particularly striking. On average,

agricultural households will move to an equilibrium that is 19.6% lower than that of non-

agricultural households. This significant difference can be explained by two related facts:

first, since most households in the surveys are subsistence farmers and net buyers, the degree

of their market participation and therefore their market purchases, is relatively limited

compared to non-agricultural households; second, food consumption expenditures, which

often represent the largest share of household total consumption expenditures, are

substantially lower for agricultural households. On the other hand, non-poor households are

expected to attain an equilibrium that is 45.8% higher than that of poor households, with an

average monthly consumption of 35,100UShs against 24,080UShs for poor households.

The location of consumption equilibria is found negatively correlated with the exposure to

food price shocks. Hence, households exposed to food price shocks are moving towards a

consumption threshold that is 6.5% lower than that of their unexposed counterparts, with

30,260UShs of consumption values against 32,360UShs. Furthermore, the more the

household is affected by food price shocks, the lower its attainable welfare equilibrium.

Concretely, households with lower exposure rates (with degree of exposure below the sample

median) can expect to reach a long term consumption dynamic equilibrium that is 15.1%

higher than that of households with high exposure rates (above the 75 percentile of the sample

value) and 5.8% higher than households with moderate exposure rates (between the median

and the 75 percentile). These sequences of welfare equilibria conform to our proposition 2

stating that the higher the degree of exposure to food price shocks, the lower the level of

attainable welfare equilibrium.

93

The average value from the different estimation methods in table 4.8.


157

Households located below the vulnerability threshold hvul can expect to reach a welfare

equilibrium on average 57.1% greater than that of households beyond the estimated critical

vulnerability index. Finally, table 4.8 shows that the geographical location also matters in

explaining the levels of consumption equilibria. For instance, the northern region of Uganda,

which is traditionally more vulnerable and with the largest proportion of poor households, is

characterized by the lowest consumption threshold at 27,180UShs on average, whereas the

better-endowed central region converges to the highest welfare level at an average of

35,420UShs.

In terms of assets accumulation process, table 4.9 reveals some similar patterns in welfare

equilibria to those of consumption: female-headed households are expected to reach lower

asset equilibria; the more educated the household head, the higher the likelihood of attaining

higher asset equilibria; non-poor households consistently converge towards higher asset

thresholds than poor households; while structurally poor regions (Northern region and to a

smaller extent eastern region) are characterized by lower asset equilibrium levels. As of

dissimilarities between the two welfare indicators, agricultural households are now moving to

higher asset equilibria than non-agricultural ones, with an asset index 1.15 against 1.12.

Finally, there seems to be only a marginal correlation between being exposed to food price

shocks and the levels of asset thresholds. Hence, the difference in asset equilibrium between

exposed and unexposed households is on average of 1.5%, compared to 7.6% when it comes

to consumption expenditures. This consistently holds when I disentangle households by their

degree of exposure to food price shocks: the asset level at equilibrium of low exposed

households exceeds that of moderately and highly exposed only by 2% and 3.3%,

respectively. Net sellers are moving towards higher asset levels than net buyers, and

households below the threshold of the vulnerability index have on average higher asset levels

than those beyond hvul .

Essay IV

158

Table 4.9 Approximate location of asset index (in PLUs) equilibria by estimation methods

Non-parametric methods Cubic

parametric

regression

(S-GMM)

Ruppert et

al.’s

penalized

splines

LOWESS Kernel linear

polynomial

regression

Kernel cubic

polynomial

regression

Mean Mean CI Mean CI Mean Mean

All sample 1.15 1.18 [0.90;1.20] 1.15 [1.00;1.17] 1.10 1.13

Male-headed households 1.19 1.20 [1.15;1.22] 1.19 [1.17;1.20] 1.13 1.15

Female-headed households 1.09 1.07 [1.02;1.10] 1.10 [1.08;1.12] 1.02 1.05

Head with no education 1.12 1.15 [1.00;1.20] 1.14 [1.12;1.17] 1.05 1.10

Head with primary educ. 1.12 1.13 [1.12;1.15] 1.15 [1.13;1.18] 1.07 1.11

Head with secondary educ. 1.23 1.22 [1.20;1.24] 1.23 [1.21;1.25] 1.18 1.19

Head with higher educ. 1.21 1.21 [1.17;1.22] 1.20 [1.16;1.21] 1.20 1.18

Agricultural households 1.15 1.15 [1.13;1.16] 1.14 [1.13;1.15] 1.16 1.14

Net sellers 1.22 1.22 [1.20;1.23] 1.21 [1.19;1.23] 1.10 1.03

Net buyers 1.12 1.13 [1.12;1.14] 1.14 [1.13;1.15] 1.07 1.00

Non-agr. households 1.11 1.11 [1.10;1.13] 1.12 [1.10;1.14] 1.12 1.12

Poor households 1.00 0.97 [0.70;1.00] 1.00 [0.98;1.10] 1.09 1.11

Non-poor households 1.19 1.19 [1.17;1.20] 1.18 [1.17;1.19] 1.12 1.12

Exposed to price shocks 1.11 1.12 [1.10;1.14] 1.13 [1.12;1.14] 1.05 1.10

High exposure 1.09 1.10 [1.07;1.13] 1.10 [1.10;1.15] 1.03 1.08

Moderate exposure 1.10 1.11 [1.09;1.14] 1.12 [1.11;1.13] 1.04 1.10

Low exposure 1.12 1.13 [1.10;1.17] 1.15 [1.14;1.20] 1.07 1.11

Unexposed to price shocks 1.13 1.14 [1.14;1.10] 1.14 [1.10;1.21] 1.07 1.12

Above the vulnerability threshold 1.06 1.00 [0.08;1.02] 1.05 [1.03;1.06] 1.15 0.97

Below the vulnerability threshold 1.18 1.18 [1.17;1.20] 1.17 [1.15;1.19] 1.07 1.01

Central region 1.25 1.23 [1.21;1.24] 1.22 [1.21;1.25] 1.21 1.20

Eastern region 1.11 1.12 [1.10;1.13] 1.13 [1.12;1.14] 1.09 1.11

Northern region 0.89 0.89 [0.85;0.90] 0.90 [0.89;0.91] 0.85 0.88

Western region 1.11 1.13 [1.12;1.14] 1.14 [1.13;1.15] 1.011 1.12

4.6.6 Sensitivity of estimation results to the definition of shock variable

In this last section, I examine whether the previous estimation results are sensitive to the

definition of the food price shock variable. In the previous sections, a household was assumed

exposed to food price shocks if its normalized residuals from equation (4.12) are positive. I

now extend this shock definition by including both negative price shocks and different cut-off


159

points. Indeed, although the sample period is characterized by increases in food prices, it is

well conceivable that some households in specific villages or districts enjoyed remarkably

average low prices between survey rounds. On the other hand, varying the cut-off for the

shock definition helps check the robustness and stability of the results as the definition of

food price shocks becomes more (less) severe. The cut-off points range from 1 to 25% of

observations falling into each tail region. For instance, with the 1% cut-off, a household is

considered as having experienced a food price shock if its standardized residuals from (4.12),

hct , is either below the 1st or above the 99

th percentile. The approximate welfare equilibria

for each selected cut-off point and econometric estimation method are presented in table 4.10.

Table 4.10 Sensitivity of welfare equilibria to the definition of the price shock variable

Exposed to food price shocks

%1 %5 %10 %25

ec ea

ec ea

ec ea

ec ea

LOWESS 30,600 1.12 30,500 1.15 30,000 1.15 31,000 1.17

Cubic Kernel 30,200 1.12 31,000 1.14 31,500 1.15 32,500 1.17

GMM 31,500 1.08 32,500 1.11 33,000 1.13 33,800 1.16

Penalized splines 33,000 1.12 33,000 1.15 34,000 1.16 33,700 1.17

Average 31,325 1.11 31,750 1.14 32,125 1.15 32,750 1.17

Observations 130 651 1,304 3,259

Unexposed to food price shocks

%1 %5 %10 %25

ec ea

ec ea

ec ea

ec ea

LOWESS 29,900 1.15 31,000 1.17 32,500 1.18 36,000 1.19

Cubic Kernel 31,000 1.15 32,500 1.18 31,700 1.17 34,500 1.20

GMM 32,000 1.16 33,500 1.16 33,500 1.17 33,800 1.18

Penalized splines 33,500 1.14 33,700 1.15 34,500 1.18 33,500 1.18

Average 31,600 1.15 32,675 1.17 33,050 1.18 34,450 1.19

Observations 6,389 5,868 5,215 3,260

Note: ec and

ea denote the approximate equilibrium locations of consumption expenditures

and asset index.

Overall, the different equilibria follow the same structure that our default measure of food

price shock: for each cut-off point , exposed households are expected to reach a lower

equilibrium than their unexposed counterparts. Furthermore, as the cut-off point increases

Essay IV

160

(decreases) or the definition of the price shock becomes less (more) severe, the welfare

thresholds increase (decrease), from 31,325UShs to 32,750UShs at %1 and %25 ,

respectively, when households experienced food price shocks. Finally, at lower level cut-off

points, the location of consumption equilibria of exposed households appears insensitive to

shifts in the cut-off points, contrarily to asset holdings. For instance, the equilibrium levels of

consumption (assets) increase by 1.36% (2.7%) for exposed households and by 3.4% (1.74%)

for unexposed households when shifts from 1 to 5%.

4.7 Conclusions

Recently, empirical studies on households’ vulnerability to covariate and idiosyncratic shocks

have been increasingly prominent, especially in developing countries. Of particular interest

have been the poverty impacts of high food prices in rural and poor communities. It has been

established that in many settings, increases in food prices were detrimental for the majority of

households in developing countries, as they are primarily pure consumers or net buyers of

agricultural products. However, most of these studies are developed under a cross-sectional

approach and therefore fall short of uncovering the potential effect of price changes on

poverty dynamics or persistent poverty. This last essay has tried to fill this empirical gap by

analyzing the structure of household welfare dynamics in a context characterized by high food

price volatility and differential exposure to food price shocks. It has particularly tested the

assumption that households that faced large increases in food prices were likely to experience

high risks of thrusting into poverty traps or converging towards lower welfare equilibria. In

order to shed light on the likely effects of differential exposure to food price shocks on

welfare growth and risks of poverty traps, this study combines advanced methods in

parametric, non-, and semi-parametric dynamic panel models using longitudinal data

collected in Uganda between 2005 and 2012 on around 2,200 households.

By means of monthly real values of consumption per adult equivalent and asset indices as

measures of welfare indicators, the empirical findings from a cubic polynomial regression

model estimated through a two-step system GMM method suggest the existence of both

nonlinearities in welfare dynamics and conditional convergence operating at the district level.

Household characteristics such as household size, gender of the household head, land size as

well as the changes in exposure to food price shocks are found to influence negatively the

growth rates of consumption expenditures. Particularly, the results show that the higher the

degree of exposure to food price shocks, the lower the rates of consumption growth, and the

decreases in these rates are more important than those consecutive to exposure to health,


161

agricultural, or income shocks. Furthermore, and similarly to previous studies (Dercon and

Christiaensen, 2011; Amare and Waibel, 2013), the assets dynamic model indicates that

structurally poor households were more vulnerable to asset shocks than structurally non-poor

and that the larger the number of assets shocks, the lower the assets accumulation growth

rates.

However, contrarily to most studies of welfare dynamics based on either consumption growth

or asset-based approaches, I find no evidence in favor of multiple welfare equilibria or

bifurcations of welfare trajectories. In contrast, consumption and asset recursion diagrams

reveal the presence of a single dynamic welfare equilibrium towards which Ugandan

households are converging. The empirical insights from parametric methods are relatively

consistent with non- and semi-parametric evidences in which welfare equilibria are located

slightly above the official poverty line. Accordingly, welfare equilibria were located at around

30,500UShs and 1.14 PLUS for consumption and asset indices, respectively. There are

different potential explanations about the absence of any consumption- or assets-based

poverty traps in Uganda, such as potential measurement errors, lack of information on other

important aspects of household life (social network, kinship ties, membership to different

organizations,...) (Giesbert and Schindler, 2012). But, as pointed out by Naschold (2013),

studies that do find evidence of poverty traps are generally characterized by relatively long

panel spells, likely to pick up long term welfare dynamics and significant differential

processes, particularly if consumption expenditures or assets holdings are moving slowly. In

our setting, although the time span between the baseline survey (2005/6) and the second

survey (2009/10) is reasonably acceptable, the follow-up surveys were conducted annually, a

particularly short period to uncover significant changes in long-run welfare dynamics.

Finally, I split the household sample into sub-groups of population to consider the possibility

of shifting welfare equilibria related to differential exposure to food price shocks, regional

location, or other households’ observables. My results suggest that, regardless of the

estimation methods selected, being exposed to food price shocks was not sufficient to push

Ugandan households into poverty traps, as recently hypothesized. However, I do find that

households exposed to price shocks are expected to converge towards lower welfare equilibria

(in terms of consumption and assets holdings) than unexposed households, though still above

the poverty line. Furthermore, the higher the degree of exposure to price shocks, the lower the

attainable equilibrium. The effects of these differential degrees of exposure to price shocks

are substantially larger on consumption than assets accumulation, at 7.6% against 1.5%.

Households living in better-off Ugandan regions, such are the Central and Western regions,

are found to settle at higher welfare equilibria than those in poor Northern regions. There is

Essay IV

162

also evidence of gender differences in welfare trajectories, with female-headed households

consistently moving to lower welfare thresholds, while highly educated and non-poor

households enjoyed higher welfare equilibria.

These empirical findings have straightforward policy implications. First, the fact that the

welfare equilibria of most households are located just slightly above the poverty lines (official

and asset-based poverty lines) implies that policy interventions should primarily focus not

only on keeping current households located above these thresholds from falling below but

also on helping them move towards higher welfare levels. As of those already below these

thresholds, and potentially below the poverty lines, safety nets mechanisms need to be

enforced in order to extricate them from the low welfare levels they are truck in.

The second implication is related to the impacts of both price and asset shocks, which are

found to negatively affect consumption expenditures and assets holdings. As is well

documented in the literature, when hit by shocks, poor households may deteriorate their

already-critical welfare conditions by modifying for example their consumption behavior to

smooth their assets (Amare and Waibel, 2013). One possible way out might be to build their

resilience to these shocks and other stressors by increasing ex ante their capacities to manage

risks and by helping them ex post to minimize the adverse consequences of shocks.

Stimulating households to engage into diversified activities (for example, combination of

farm and non- or off-farm activities) or developing targeted programs that aim at improving

the structural characteristics of the country such as better access to land, credit, or insurance

markets, improvements in health coverage or infrastructure coverage may well reduce the

vulnerability of households to both food price and asset shocks.

163

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Appendices

185

APPENDICES


186

Appendix A

Additional data and estimation results for Essay I


187

Appendix A.1 Monthly price volatility plots (January 2000 – December 2012)

0

.05

.1.1

5.2

.25

Mo

nth

ly v

ola

tility

pri

ce, M

ato

oke

Jan00 Jan02 Jan04 Jan06 Jan08 Jan10 Jan12

Monthly price volatility

Matooke

0.1

.2.3



Cassava

0

.05

.1.1

5.2

.25



Maize

0.1

.2.3

.4



Sweet potatoes

0.1

.2.3

.4



Beans

0

.05

.1.1

5



Millet flour

Appendices

188

Appendix A.2 Monthly price volatility by main agricultural seasons, 2000m1 – 2012m12

Agricultural

seasons

Months Matooke cassava Maize Sweet

potatoes

Beans Millet

flour

Average

Planting 1

March 0.057 0.053 0.043 0.072 0.041 0.034 0.050

April 0.075 0.069 0.049 0.083 0.067 0.032 0.063

May 0.101 0.046 0.075 0.081 0.058 0.028 0.065

Average 0.078 0.056 0.056 0.079 0.055 0.031 0.059

Harvest 1

June 0.056 0.053 0.093 0.121 0.097 0.038 0.076

July 0.087 0.047 0.087 0.110 0.069 0.032 0.072

August 0.048 0.036 0.078 0.091 0.051 0.025 0.055

Average 0.064 0.045 0.086 0.108 0.072 0.031 0.068

Planting 2

September 0.080 0.065 0.065 0.087 0.172 0.033 0.084

October 0.083 0.055 0.068 0.049 0.092 0.027 0.062

November 0.043 0.044 0.112 0.066 0.064 0.024 0.059

Average 0.068 0.055 0.081 0.068 0.109 0.028 0.068

Harvest 2

December 0.079 0.039 0.078 0.061 0.045 0.015 0.053

January 0.070 0.030 0.081 0.090 0.050 0.028 0.058

February 0.011 0.062 0.071 0.066 0.035 0.031 0.046

Average 0.084 0.043 0.076 0.072 0.043 0.025 0.057

Conclusion H1<P2

<P1<H2

H2<H1

<P2<P1

P2<H2

<P2<H2

P2<H2

<P1<H1

H2<P1

<H1<P2

H2<P2

<P1=H1

H2<P1

<H2=P2

Note: P1, P2, H1, and H2 denote respectively the first and second planting seasons, and the first and second harvest

seasons in Uganda.


189

Appendix A.3 Estimated results of Multivariate VARs


potatoes

Beans Millet

flour

Matooket-1 0.689

(0.076)***

-0.156

(0.062)**

-0.082

(0.082)

0.093

(0.109)

-0.132

(0.068)*

0.029

(0.038)

Cassavat-1 -0.013

(0.108)

0.756

(0.088)***

-0.180

(0.106)*

0.328

(0.085)***

-0.287

(0.126)**

-0.063

(0.054)

Maizet-1 -0.006

(0.074)

0.026

(0.060)

0.375

(0.080)***

0.026

(0.107)

0.058

(0.087)

-0.059

(0.027)*

Sweet potatoest-1 0.079

(0.048)*

0.106

(0.048)**

0.015

(0.064)

0.458

(0.085)***

0.016

(0.069)

0.024

(0.030)

Beanst-1 -0.023

(0.066)

-0.031

(0.054)

0.108

(0.051)*

0.057

(0.096)

0.507

(0.078)***

-0.017

(0.033)

Millet flourt-1 0.178

(0.153)

-0.110

(0.125)

-0.249

(0.145)*

0.046

(0.221)

-0.011

(0.179)

0.638

(0.077)***

Matooket-2 0.437

(0.080)***

0.023

(0.065)

-0.035

(0.086)

0.098

(0.116)

-0.116

(0.094)

0.005

(0.040)

Cassavat-2 0.031

(0.108)

0.195

(0.088)**

-0.062

(0.116)

0.082

(0.156)

0.046

(0.126)

-0.059

(0.054)

Maizet-2 -0.010

(0.074)

-0.024

(0.060)

0.274

(0.080)***

-0.017

(0.107)

0.008

(0.087)

-0.033

(0.037)

Sweet potatoest-2 0.031

(0.059)

0.053

(0.048)

-0.063

(0.064)

0.146

(0.085)*

0.015

(0.069)

-0.036

(0.030)

Beanst-2 -0.014

(0.064)

0.027

(0.052)

0.199

(0.069)***

0.010

(0.092)

0.413

(0.075)***

-0.009

(0.032)

Millet flourt-2 0.080

(0.154)

-0.180

(0.126)

-0.400

(0.166)***

-0.358

(0.202)*

-0.056

(0.180)

0.290

(0.077)***

break -0.008

(0.025)

0.041

(0.020)**

-0.006

(0.027)

0.018

(0.036)

-0.021

(0.029)

0.032

(0.012)**

Cons 0.001

(0.005)

-0.001

(0.004)

0.000

(0.005)

-0.001

(0.007)

0.001

(0.006)

-0.001

(0.002)

Adjusted R2

0.390 0.432 0.300 0.275 0.402 0.359

Note: Standard errors into brackets. ***

,**

,* denote significance levels at 1, 5, and 10%, respectively

Appendices

190

Appendix A.4 Matrix of pairwise correlations of food price volatilities


potatoes

Beans Millet

flour

Matooke 1

Cassava -0.255

(0.001)***

1

Maize 0.191

(0.018)**

-0.303

(0.000)***

1

Sweet potatoes 0.076

(0.347)

0.315

(0.000)***

0.283

(0.000)***

1

Beans -0.010

(0.898)

0.114

(0.157)

0.089

(0.266)

0.136

(0.091)*

1

Millet flour 0.022

(0.787)

-0.264

(0.001)***

0.127

(0.115)

0.139

(0.086)*

-0.030

(0.712)

1

Note: ***

, **

, and * denote significance levels at 1, 5, and 10%, respectively


191

Appendix B

Additional data and estimation results for Essay II

Appendices

192

Appendix B.1 Testing and correcting for attrition in the Uganda National Panel Surveys

The prominence of available panel data in the recent decades has helped researchers to undertake

the analysis of economic relationships that would have otherwise been impossible. Indeed, among

the main advantages of longitudinal data, they usually provide the researcher with a large number of

data points (N*T), thereby increasing both the degrees of freedom and the efficiency of econometric

estimations by reducing the collinearity of explanatory variables. By tracking the same individuals

or households over an extended period of time, panel data can control for their unobserved

heterogeneity, investigate the dynamics of their welfare indicators such consumption, income, or

asset holdings, and test for some microeconomic theories such as the Permanent Income Hypothesis

(PIH), and consumption or asset smoothing.

Despite the well-recognized and documented advantages of panel data, they generally suffer from

sample selection and attrition. The former arises when the observed sample is not a random draw

from the population of interest which can potentially lead to inconsistency and bias in the

estimation of parameters of interest. The latter, often dubbed “the panel researcher’s nightmare”

(Winkles and Withers, 2000), arises when the individuals or households that have dropped out of

the panel are systematically different from those who have stayed. Consequently, the results based

on the remained surveyed individuals may no longer be representative of the original population. If

the drop-out is entirely random, then there is nothing further the researcher can do.

In the present appendix, we present the procedure used to test and correct for the attrition bias94

. To

test for the consistency of the results, two tests are successively presented: the attrition probits’ tests

of Fitzgerald et al. (1998) and the pooling tests of Becketti, Gould, Lillard and Welch (1988)

(henceforth, BGLW test). The correction of attrition bias is then done through the inverse

probability weighting (IPW) procedure (Fitzgerald et al., 1998; Wooldridge, 2002)

Tests of attrition bias

In table B.1.1, we summarize the number of population (and households) in the Uganda National

Panel Surveys (UNPS) used in the present study as well as the attrition rate from the original

sample. Out of the 3,123 households (representing 16,759 individuals) that were initially sampled

for the panel dataset, 83.5% (or 2,607 households) were successively tracked in 2009/10 (UNPS-

2010). In the third survey, this percent slightly decreased to 82.1% (2,564 households) and in the

UNPS-2012, around 1,000 households were not successively tracked. These numbers give an

attrition rate relatively high (above 15%).

94

The sample design of the LSMS (Living Standards Measurement Surveys) and LSMS-ISA (LSMS-Integrated Surveys on Agriculture) of which the UNPS are part eliminates or at least minimize the risk of sample selection problems.


193

Table B.1.1 Summary of the number of population and households in the UNPS and the attrition rate

Population

interviewed

Number of

households

sampled

Number of households

successively tracked

Attrition rate from

the original

sample

UNPS-2006: Baseline survey 16,759 3,123 3,123 0.00

UNPS-2010 17,511 3,123 2,607 16.30

UNPS-2011 18,810 3,123 2,564 17.90

UNPS-2012 16,139 3,123 2,356 24.56

To test whether the observed attrition was random, we estimate a probit model (Fitzgerald et al., 1998) in

which the dependent variable (attrition) takes 1 if the household drops out of the sample after the

first wave and 0 otherwise95

. The independent variables are all baseline variables likely to affect the

attrition. Among these variables, we include household characteristics such as household size,

household composition (proportions of household members between 0 and 4, 5-14, 19-34, 35-54,

and 55 and beyond), monthly real values of consumption per adult equivalent, the estimated values

of productive assets, and the cultivated land size (in acres). We also add household head

characteristics (years of education, age and its squared value, and sex), regional dummies, as well as

the household’s net position in the food market.

Results of the probit model, reported in table B.1.2, show that most explanatory variables negatively

affected the probability of dropping out of the panel after the first survey. It appears that on average

households that were most likely to be re-interviewed in all waves have significantly larger family,

have a head significantly older, and are essentially agricultural (all the estimated coefficients

associated with different net position in the food market are negative). However, monthly values of

consumption significantly and positively influence the probability of dropping out of the sample. In

addition, the value of the pseudo R-squared from the attrition probit is only 14.5%, implying

baseline variables only explain about 14.5% of the panel attrition between 2005/6 and 2011/12.

To perform the BGLW test, we first interact the dependent variable from table B.1.2 (attrition) with

all the independent variables from the attrition probit and regress the log of monthly real values of

consumption on household and auxiliary variables and their interactions with the attrition variable

(Outes-Leon and Dercon, 2011; Baulch and Quisumbing, 2011). We then perform an F-test to

check whether the attrition dummy variable and its interactions with household and auxiliary

variables are jointly significant to zero, with the null hypothesis that the observed attrition status of

95

In doing so, we are only treating a special form of attrition in which attrition is an absorbing state (Wooldridge, 2002: 585), meaning that once individuals/households have dropped out of the survey (at t=2 or beyond), they cannot reenter. In the general case, surveyed units can reenter the sample after leaving. In the UNPS, only 20 households reenter after leaving in 2009/10.

Appendices

194

a household is random. We find an F-test of 4.63 with a p-value of 0.000, meaning that the

observed attrition in the Ugandan panel dataset was primarily non-random and therefore needs to be

corrected for.

Table B.1.2 Attrition Probit for household consumption (n=3,123)

Coefficient Standard errors (a) z-statistic (p-value)

Years of education -0.004 0.009 -0.50 (0.619)

Age -0.037 0.012 -3.09 (0.002)***

Age squared 0.000 0.000 2.57 (0.010)***

Sex: 1 if female-headed 0.032 0.061 0.52 (0.602)

Household size -0.017 0.017 -1.01 (0.313)

% of household members between: 0-4 years -0.873 0.270 -3.23 (0.001)***

5-14 years -0.898 0.247 -3.64 (0.000)***

15-19 years -0.712 0.269 -2.65 (0.008)***

20-34 years -0.401 0.219 -1.84 (0.066)*

35-54 years -0.245 0.207 -1.19 (0.235)

Land size (acres) -0.004 0.004 -1.17 (0.241)

Value of assets (log) -0.029 0.022 -1.30 (0.195)

Region dummy: 1 if Eastern region -0.004 0.081 -0.04 (0.964)

1 if Northern region -0.163 0.096 -1.70 (0.090)*

1 if Western region 0.343 0.096 3.58 (0.000)***

Monthly consumption (log) 0.154 0.053 2.89 (0.004)***

Net food market position: 1 if SNS -0.900 0.080 -9.99 (0.000)***

1 if SNB -0.722 0.076 -9.46 (0.000)***

1 if INS -0.953 0.183 -5.19 (0.000)***

1 if INB -0.843 0.175 -4.82 (0.000)***

Constant 0.109 0.631 0.17 (0.862)

Pseudo – R squared 0.145

Log Pseudolikelihood -1,440.117

Note: (a): clustered-robust standard errors, at the village level (322 clusters). SNS, SNB, INS, and INB denote

respectively, significant net sellers, significant net buyers, insignificant net sellers, and insignificant net buyers. ***

and * denote significance levels at 1 and 10%, respectively.

Computing Inverse Probability Weights (IPW) to correct for attrition bias

To correct for the non-randomness of the attrition, we follow Moffit et al. (1999) by computing

inverse probability weights (IPW). The procedure consists in first calculating the predicted

probabilities from the unrestricted retention probit model using the same set of variables as in table

B.1.2 and then re-estimating the same model by excluding household demographics and head


195

characteristics. The IPW are then computed as the ratio between the restricted and unrestricted

probabilities. The average value of the IPW was 1.331 with a standard deviation of 0.742. The IPW

for non-attritors were found to be larger than those of attritors, with 1.429 against 1.010. These IPW

are then using in all econometric estimations to account for the attrition bias.

Figure B.1.1 Kernel distribution of IPW for attritors and non-attritors

Appendices

196

Appendix B.2 Demand elasticities under separability

Type of

elasticity

Symbol Formula

Conditional

expenditure

elasticity

i *

1

i

ii

s

where

Pa

x

Pb

i

iii ln)(

2 and iiii ss *

Conditional

Marshallian

elasticity

uij

ij

i

ijuij

s

*

where

2

1 )(ln

)(ln

Pa

x

Pbp

s

iin

k

kjkjiij

i

i

ijij

and ij = 1 if ji and 0 otherwise.

Conditional

Hicksian

elasticity

cij *

* ji

i

ijcij s

s

Source: Banks et al., 1997; Shonkwiler and Yen, 1999


197

Appendix B.3 Estimated average shadow elasticities by food net market position

Net market

position ipwE /*

*/ wcE i xwE /*

Matooke

B 0.164 (0.047)***

0.145 (0.013)***

-0.033 (0.018)**

C 0.087 (0.027)***

0.122 (0.022)***

-0.062 (0.018)***

D -0.050 (0.001)***

-0.124 (0.013)***

0.127 (0.068)*

E

0.029 (0.138) -0.120 (0.014)***

0.103 (0.059)*

Cassava

B 0.070 (0.050) 0.070 (0.020)**

-0.033 (0.018)**

C 0.117 (0.037)***

0.076 (0.018)***

-0.062 (0.018)***

D 0.051 (0.021)*

-0.042 (0.022)*

0.127 (0.068)*

E

0.313 (0.149)**

-0.051 (0.019)***

0.103 (0.059)*

Potatoes

B -0.034 (0.046) 0.070 (0.019)**

-0.033 (0.018)**

C 0.083 (0.032)***

0.046 (0.024)*

-0.062 (0.018)***

D -0.066 (0.013)***

-0.041 (0.021)*

0.127 (0.068)*

E

0.237 (0.132)*

- 0.024 (0.023) 0.103 (0.059)*

Maize

B -0.222 (0.064)***

0.046 (0.026)*

-0.033 (0.018)**

C 0.033 (0.042) 0.071 (0.019)***

-0.062 (0.018)***

D -0.046 (0.017)**

0.039 (0.023) 0.127 (0.068)*

E

-0.540 (0.176)***

0.047 (0.021)**

0.103 (0.059)*

Bean

B 0.012 (0.063) 0.009 (0.015) -0.033 (0.018)**

C 0.051 (0.040) -0.011 (0.016) -0.062 (0.018)***

D -0.073 (0.019)***

-0.017 (0.016) 0.127 (0.068)*

E

0.209 (0.106)*

-0.011 (0.015) 0.103 (0.059)*

Meat and

fish

B 0.069 (0.051) 0.087 (0.013)***

-0.033 (0.018)**

C 0.057 (0.025)**

0.089 (0.012)***

-0.062 (0.018)***

D -0.241 (0.109)**

-0.075 (0.010)***

0.127 (0.068)*

E

-0.133 (0.147) -0.064 (0.012)***

0.103 (0.059)*

Fruits and

vegetables

B 0.104 (0.051)**

-0.018 (0.015) -0.033 (0.018)**

C -0.099 (0.035)***

0.005 (0.012) -0.062 (0.018)***

D 0.063 (0.014)***

-0.036 (0.015)**

0.127 (0.068)*

E

0.132 (0.085)*

-0.009 (0.013) 0.103 (0.059)*

Fats and

oils

B 0.073 (0.063) 0.015 (0.018) -0.033 (0.018)**

C 0.060 (0.031)* 0.032 (0.015)

* -0.062 (0.018)

***

D -0.194 (0.026)***

-0.016 (0.016) 0.127 (0.068)*

E

0.249 (0.157)*

-0.015 (0.016) 0.103 (0.059)*

Other

foods (a)

B 0.120 (0.073)*

0.045 (0.014)**

-0.033 (0.018)**

C 0.106 (0.050)**

0.039 (0.014)*

-0.062 (0.018)***

D 0.302 (0.131)**

-0.009 (0.016) 0.127 (0.068)*

E

0.042 (0.023)* 0.020 (0.015) 0.103 (0.059)

*

Alcohol

and

tobacco

B 0.030 (0.024) -0.094 (0.038)**

-0.033 (0.018)**

C 0.007 (0.017) -0.068 (0.033)*

-0.062 (0.018)***

D 0.067 (0.033)**

-0.080 (0.033)**

0.127 (0.068)*

C

0.005 (0.065) -0.112 (0.038)***

0.103 (0.059)*

Note: B: Significant net sellers; C: significant net buyers, D: insignificant net sellers, and E: insignificant net buyers.

(***

), (**

), and (*) denote significance levels at 1, 5, and 10% respectively. Standard errors are reported into brackets.

Source : Own computations using UNPS data

Appendices

198

Appendix C

Additional data and estimation results for Essay III


199

Appendix C.1 Patterns of crop choice combinations, 2005 – 2012

Binary sixplet

Number of farmers

W1 W2 W3 W4 Pooled Binary sixplet W1 W2 W3 W4 Pooled

(1, 0, 0, 0, 0, 0)

10

5

10

7

32

(0, 1, 1, 0, 1, 0)

56

48

64

55

223

(0, 1, 0, 0, 0, 0) 11 9 22 14 56 (0, 1, 1, 0, 0, 1) 38 39 35 33 145

(0, 0, 1, 0, 0, 0) 15 11 4 10 40 (0, 1, 0, 1, 1, 0) 7 15 31 18 71

(0, 0, 0, 1, 0, 0) 7 6 3 2 18 (0, 1, 0, 1, 0, 1) 22 30 42 31 125

(0, 0, 0, 0, 1, 0) 7 7 4 6 24 (0, 1, 0, 0, 1, 1) 12 16 14 17 59

(0, 0, 0, 0, 0, 1) 26 22 14 28 90 (0, 0, 1, 1, 1, 0) 17 11 18 26 72

(1, 1, 0, 0, 0, 0) 3 10 14 9 36 (0, 0, 1, 1, 0, 1) 17 6 5 9 37

(1, 0, 1, 0, 0, 0) 4 5 4 4 17 (0, 0, 0, 1, 1, 1) 16 19 14 17 66

(1, 0, 0, 1, 0, 0) 8 12 5 6 31 (1, 1, 1, 1, 0, 0) 22 31 23 12 88

(1, 0, 0, 0, 1, 0) 20 20 17 23 80 (1, 1, 1, 0, 1, 0) 45 75 77 80 277

(1, 0, 0, 0, 0, 1) 2 1 0 2 5 (1, 1, 1, 0, 0, 1) 10 4 2 1 17

(0, 1, 1, 0, 0, 0) 31 20 38 38 127 (1, 0, 1, 1, 1, 0) 44 37 39 61 181

(0, 1, 0, 1, 0, 0) 6 16 18 6 46 (1, 0, 1, 0, 1, 1) 23 18 23 17 81

(0, 1, 0, 0, 1, 0) 16 13 15 28 72 (1, 1, 0, 0, 1, 1) 21 17 19 19 76

(0, 1, 0, 0, 0, 1) 31 35 22 40 128 (1, 1, 0, 1, 0, 1) 7 3 4 3 17

(0, 0, 1, 1, 0, 0) 14 7 5 4 30 (1, 0, 0, 1, 0, 1) 7 12 6 63 88

(0, 0, 1, 0, 1, 0) 26 29 19 33 107 (1, 1, 0, 1, 1, 0) 19 31 58 34 142

(0, 0, 1, 0, 0, 1) 46 31 41 34 152 (1, 0, 1, 1, 0, 1) 1 1 3 1 6

(0, 0, 0, 1, 1, 0) 7 7 4 6 24 (1, 0, 0, 1, 1, 1) 19 27 23 29 98

(0, 0, 0, 1, 0, 1) 7 6 1 2 16 (0, 1, 1, 1, 1, 0) 81 92 102 91 366

(0, 0, 0, 0, 1, 1) 11 10 3 6 30 (0, 1, 0, 1, 1, 1) 19 23 16 17 75

(1, 1, 1, 0, 0, 0) 10 7 17 6 40 (0, 1, 1, 0, 1, 1) 52 39 24 42 157

(1, 1, 0, 1, 0, 0) 6 7 12 8 33 (0, 1, 1, 1, 0, 1) 70 90 60 49 269

(1, 1, 0, 0, 1, 0) 16 18 36 39 109 (0, 0, 1, 1,1 , 1) 16 22 16 10 64

(1, 1, 0, 0, 0, 1) 2 1 2 2 7 (1, 1, 1, 1, 1, 0) 182 189 218 255 844

(1, 0, 1, 1, 0, 0) 5 7 3 4 19 (1, 1, 1, 1, 0, 1) 30 11 9 6 56

(1, 0, 1, 0, 1, 0) 68 61 43 57 229 (1, 1, 1, 0, 1, 1) 21 17 19 19 76

(1, 0, 1, 0, 0, 1) 3 1 1 0 5 (1, 1, 0, 1, 1, 1) 13 19 16 10 58

(1, 0, 0, 1, 1, 0) 10 24 14 26 74 (1, 0, 1, 1, 1, 1) 40 20 26 25 111

(1, 0, 0, 1, 0, 1) 1 1 2 1 5 (0, 1, 1, 1, 1, 1) 74 97 78 55 304

(1, 0, 0, 0, 1, 1) 5 17 10 16 48 (1, 1, 1, 1, 1, 1) 116 69 70 42 297

(0, 1, 1, 1, 0, 0) 36 37 38 30 141 Total 1,587 1,579 1,589 1,581 6336

Note: Each element in the sixplet is a binary variable for the crop combination Matooke – Cassava – Maize –

Potatoes – Beans - Other cereals having 1 if the specific crop was grown by the farmer and 0 otherwise. W1 to W4

denote the 4 panel waves used. The “total” row gives the sum for each wave. The number of farmers that did not

grow any of the selected crops (the omitted category (0, 0, 0, 0, 0, 0) can be obtained by the difference between

the sample size (1,598 per wave) and the above “total” row.

Appendices

200

Appendix C.2 Farmer’s characteristics by GPS measurement status (2005/6 and 2009/10)

2005/6a

2009/10a

A B C D A B C D

Plot size

GPS-based

areas (acres)

3.249 3.249 - 2.644 2.644 -

Farmer’s self

report (acres)

3.984 3.136 9.476 -6.340** 3.025 2.589 4.827 -2.237***

Number of

plots

1.935 1.998 1.534 0.464*** 2.011 2.058 1.824 0.233***

Plot ouput and

input use

Total value of

harvest (UShs)

814,910.8 810,039.7 846,605.4 -36,565.7 2,018,187 2,036,901 1,943,330 93,571*

Total value of

inputs (UShs)

83,880.23 68,994.05 180,615.8 -111,621.75** 61,036.43 59,306.45 67,956.33 -8,649.88*

Plot location

(km)

1.535 .946 5.379 -4.434*** - - - -

Less than 15

min

- - - - 0.695 0.755 0.416 0.339***

Between 15-30

min

- - - - 0.115 0.112 0.129 -0.017

Between 30-60

min

- - - - 0.081 0.062 0.169 -0.107***

Between 1-2

hours

- - - - 0.057 0.041 0.132 -0.091***

Tenure system 0.025 0.008 0.101 -0.093***

Freehold 0.070 0.074 0.049 0.025* 0.387 0.421 0.249 0.172***

Leasehold 0.027 0.026 0.033 -0.007 0.039 0.034 0.060 -0.026**

Customary 0.706 0.714 0.656 0.058** 0.496 0.475 0.576 -0.100***

Soil quality

Good 0.475 0.473 0.488 -0.015 0.568 0.567 0.573 -0.006

Fair 0.433 0.431 0.442 -0.011 0.314 0.319 0.294 0.024

Poor 0.103 0.107 0.076 0.031*** 0.093 0.095 0.085 0.010

Plot slope

Gentile 0.359 0.367 0.304 0.064** 0.389 0.394 0.369 0.025***

Flat 0.501 0.494 0.545 -0.051* 0.444 0.439 0.464 -0.025

Other (Hilly,

steep, valley)

0.155 0.154 0.158 -0.004 0.144 0.149 0.119 0.030*

Household

characteristics

Household size 5.884 5.867 5.993 -0.126 6.708 6.706 6.719 -0.011

Age of the

head

43.686 44.172 40.544 3.628*** 46.588 47.239 43.900 3.338***

Dependency

ratio

1.327 1.360 1.124 0.236*** 1.525 1.570 1.345 0.224***

Education of

the head

4.833 4.657 5.970 -1.313*** 4.798 4.591 5.725 -1.134***

Sex of the head 0.734 0.731 0.751 -0.020 0.721 0.721 0.719 0.002

Central 0.218 0.201 0.292 -0.086*** 0.215 0.203 0.261 -0.058***

Eastern 0.262 0.273 0.193 0.079*** 0.256 0.258 0.246 0.013

Northern 0.261 0.253 0.311 -0.059** 0.279 0.246 0.414 -0.168***

Western 0.259 0.268 0.203 0.065*** 0.243 0.289 0.055 0.234***

Non-farm

income

598,177.6 468,997.7 1,4338,824 -964,826.3*** 538,240.5 530,907.9 568,566.8 -37,658.9**

Note:* A, B, and C refer respectively to the entire sample, the sample restricted to plots with observed GPS-based

measures, and plots without GPS-based measures. The last column D computes the difference between B and C.


201

Appendix C.3 Farmer’s characteristics by GPS measurement status (2010/11 and 2011/12)

2010/11

2011/12

A B C D A B C D

Plot size

GPS-based

areas (acres)

4.202 4.202 - - 2.377 2.377- - -

Farmer’s self

report (acres)

2.729 2.401 3.944 -1.543*** 2.622 2.444 2.879 -0.435*

Number of

plots

1.779 1.794 1.724 0.071 1.854 1.884 1.810 0.073

Plot ouput and

input use

Total value of

harvest (UShs)

967,971.4 940,134.5 1,070,611 -130,476.5 1,401,579 1,281,891 1,574,111 -292,220

Total value of

inputs (UShs)

57,016.6 50,640.78 80,525.41 -

29,884.63***

54,304.94 47,756.04 63,745 -15,989.2***

Less than 15

min

0.708 0.776 0.456 0.320*** 0.691 0.793 0.545 0.249***

Between 15-

30 min

0.133 0.120 0.182 -0.063*** 0.199 0.196 0.204 -0.007

Between 30-

60 min

0.086 0.070 0.143 -0.073*** 0.185 0.152 0.233 -0.082***

Between 1-2

hours

0.050 0.026 0.140 -0.114*** 0.099 0.080 0.126 -0.046***

Tenure system

Freehold 0.412 0.456 0.249 0.207*** 0.347 0.392 0.283 0.109***

Leasehold 0.019 0.022 0.010 0.011** 0.047 0.041 0.055 -0.014**

Customary 0.538 0.492 0.705 -0.213*** 0.545 0.533 0.562 -0.029*

Soil quality

Good 0.612 0.592 0.687 -0.095*** 0.590 0.608 0.564 0.045***

Fair 0.349 0.367 0.285 0.082*** 0.464 0.459 0.470 -0.011

Poor 0.040 0.045 0.023 0.021*** 0.122 0.124 0.119 0.004

Plot slope

Gentile 0.379 0.389 0.343 0.045** 0.354 0.363 0.342 0.021*

Flat 0.487 0.479 0.518 -0.039* 0.466 0.490 0.433 0.057***

Other (Hilly,

steep, valley)

0.137 0.138 0.133 0.004 0.122 0.129 0.112 0.017*

Household

characteristics

Household

size

7.533 7.488 7.703 -0.215 8.114 8.029 8.239 -0.210*

Age of the

head

48.537 48.774 47.659 1.115* 48.633 49.589 47.254 2.335***

Dependency

ratio

1.709 1.722 1.663 0.059 1.907 1.809 2.048 -0.239***

Education of

the head

5.110 4.958 5.674 -0.717*** 4.811 4.596 5.120 -0.524***

Sex of the

head

0.720 0.721 0.718 0.003 0.714 0.718 0.707 0.011

Central 0.207 0.226 0.134 0.092*** 0.201 0.160 0.260 -0.101***

Eastern 0.266 0.256 0.305 -0.049** 0.256 0.249 0.267 -0.018

Northern 0.285 0.246 0.426 -0.059*** 0.295 0.281 0.314 -0.033**

Western 0.239 0.271 0.121 0.149*** 0.248 0.311 0.158 0.152***

Non-farm

income

537,708.8 540,858.1 526,015.1 14,843 659,108.2 405,719.4 1,024,370 -618,650.6***

Note:* A, B, and C refer respectively to the entire sample, the sample restricted to plots with observed GPS-based

measures, and plots without GPS-based measures. The last column D computes the difference between B and C.

Appendices

202

Appendix C.4 OLS estimation results of Observed GPS-based plot area measures (in acres)

Dependent variable:

Observed

GPS-based areas (acres)

2005/6 2009/10 2010/11 2011/12

Plot size

Farmer’s self report (acres) 0.959 (0.021)*** 0.922 (0.14)*** 0.901 (0.150)*** 0.888 (0.201)***

Number of plots -0.898 (0.345)*** -0.526

(0.099)***

-0.882 (0.081)*** -0.305 (0.139)**

Plot output and input use

Total value of harvest

(UShs)

-0.004 (0.243) 0.084 (0.042)** 0.165 (0.054)*** 0.127 (0.114)

Total value of inputs (UShs) 0.006 (0.111) 0.122 (0.034)*** 0.091 (0.188) 0.066 (0.039)*

Plot location (km) -0.149 (0.154) - - -

Less than 15 min - -0.343

(0.049)***

-0.255 (0.055)*** 0.230 (0.175)*

Between 15-30 min - 0.574 (0.617) 0.026 (0.084) 0.030 (0.196)

Between 30-60 min - 0.367 (0.075)*** 0.076 (0.010)*** -0.153 (0.184)

Tenure system

Freehold 0.196 (11.442) -0.015 (0.723) -0.089 (0.069) -0.021 (0.029)

Leasehold 0.926 (0.572) -0.512 (0.912) -0.068 (0.087) -0.076 (0.030)***

Customary -0.075 (1.661) 0.378 (0.748) -0.219 (0.704) -0.344 (0.366)

Soil quality

Good 1.661 (1.357) -0.153 (0.373) 0.428 (0.324) 0.191 (0.188)

Fair 2.247 (1.371)* -0.794 (0.399)** -0.709 (0.441)* -0.299 (0.117)**

Plot slope

Gentile -1.214 (1.313) 0.171 (0.360) 0.082 (0.098) 0.222 (0.192)

Flat -1.674 (1.317) -0.455 (0.363) -0.300 (0.146)* -0.299 (0.217)


Household size 0.393 (0.167)** 0.198 (0.038)*** 0.214 (0.193) 0.109 (0.057)*

Age of the head 0.016 (0.029) 0.020 (0.008)** 0.042 (0.038) -0.001 (0.005)

Dependency ratio -0.314 (0.438) -0.140 (0.108) -0.615 (0.341)* -0.077 (0.064)

Education of the head 0.016 (0.133) 0.031 (0.036) 0.035 (0.170) -0.031 (0.029)

Sex of the head 0.924 (1.252) 0.044 (0.056) 0.083 (0.051) 0.076 (0.003)***

Central -0.237 (0.045)*** 0.055 (0.356) -0.071 (0.004)*** -0.032 (0.001)***

Eastern 1.368 (1.222) 0.449 (0.521) -0.259 (0.794) -0.247 (0.286)

Northern 0.593 (0.035)*** 0.079 (0.005)*** 0.081 (0.125) 0.046 (0.028)*

Non-farm income -0.013 (0.041) -0.009 (0.081) -0.002 (0.053) 0.001 (0.004)

Multiple imputation results

Observed GPS-Based areas 3.249 2.467 4.202 2.377

Imputed GPS-Based areas 3.625 2.556 4.516 2.412


203

Appendix C.5 Estimated ARIMA models for monthly real price series 1999 (9) – 2012 (12)

Commodity ARIMA results(a)

Matooke tt LpLL 23 413.011515.01

(0.047) (0.039)

Cassava tt LLpLL 22 411.0396.011732.01

(0.093) (0.089) (0.046)

Maize tt LpLL 122.011965.01

(0.021) (0.047)

Potatoes tt LLpLL 23 887.0522.011770.01

(0.049) (0.047) (0.049)

Beans tt LpLL 654.011812.01 3

(0.052) (0.063)

Other cereals (rice, millet,

sorghum) tt LpLL 23 171.011885.01

(0.027) (0.026)

Note: (a): The general ARIMA model has the following form: tt

dLBpLLA 1 , where

p

p LLLLA ...1 2

21 and q

q LLLLB ...1 2

21 are polynomials in lag

operator L ; t are errors terms assumed to be white noise. The Box-Jenkins methodology has been used to

determine the values of p (autoregressive terms) and q (moving average terms) in the ARMA (p, q) process

through the Bayesian information criteria (BIC). d (the order of integration of the price series tp ) was 1 for

all commodities. Standard errors are reported below each ARIMA specification.

Appendices

204

Appendix C.6 Unbiasedness tests of expected-price formation hypotheses (OLS estimation)

cmdt Naive expectations model Adaptive expectations model

Unbiasedness Unbiasedness

F –

Stat.

2

adjR F-Stat Reject

?0H

F –

Stat.

2

adjR F-Stat Reject

?0H

1k 167.384

(12.727)

0.491

(0.037)

179.41

0.284 81.16 Yes 123.235

(15.781)

0.640

(0.046)

189.44 0.254 31.25 Yes

2k 56.806

(11.228)

0.911

(0.026)

1268.92 0.679 15.17 Yes 21.575

(12.758)

1.025

(0.030)

1193.94 0.683 16.37 Yes

3k 109.139

(7.343)

0.843

(0.021)

1537.45 0.646 168.29 Yes 53.565

(5.602)

0.974

(0.017)

3504.25 0.674 96.96 Yes

4k 108.574

(6.991)

0.706

(0.025)

754.72 0.487 120.77 Yes 92.901

(10.508)

0.763

(0.016)

2150.11 0.420 131.83

Yes

5k 161.831

(15.409)

0.817

(0.027)

908.10 0.669 170.66 Yes 91.454

(11.721)

0.929

(0.023)

1630.09 0.737 41.48 Yes

6k 255.321

(137.682)

0.768

(0.143)

28.76 0.544 5.15 No 104.109

(64.109)

0.964

(0.068)

200.52 0.606 23.36 Yes

Quasi-rational expectations model Mixed expectations model (a)

Unbiasedness Unbiasedness

F –

Stat.

2

adjR F-Stat Reject

?0H

F –

Stat.

2

adjR F-Stat Reject

?0H

1k 19.187

(5.727)

1.059

(0.015)

4922.38 0.550 10.53 Yes 5.086

(8.085)

1.031

(0.029)

123.32 0.832 5.01 No

2k 34.311

(6.536)

1.086

(0.013)

6721.69 0.798 22.04 Yes 0.888

(3.081)

1.043

(0.015)

483.29 0.775 5.82 No

3k 9.349

(4.891)

1.018

(0.009)

1301.91 0.889 4.23 No 4.945

(2.319)

1.013

(0.005)

475.83 0.834 5.54 No

4k 18.170

(2.007)

1.051

(0.008)

2188.59 0.736 50.16 Yes 1.977

(3.772)

1.012

(0.008)

176.58 0.619 5.26 No

5k 56.832

(9.148)

1.077

(0.011)

8661.10 0.828 30.04 Yes 9.549

(5.937)

1.026

(0.010)

100.34 0.807 4.13 No

6k 38.812

(14.373)

1.043

(0.013)

6149.52 0.691 28.11 Yes 4.555

(13.295)

1.026

(0.016)

452.48 0.700 2.84 No

Note: 1k , 2k , 3k , 4k , 5k , and 6k refer respectively to matooke cassava, maize, potatoes, beans, and other

cereals. Standard errors into brackets.

(a) For each price series, different values of were tested ( 9.0;...;2.0;1.0 ). Here, I only report the

model with the “optimal” weights (best statistical fits): 0.3 for cassava and beans; 0.4 for matooke and

potatoes; 0.5 for maize and 0.6 for other cereals.


205

Appendix C.7 Definition and descriptive statistics of relevant variables

Definition of variables


Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD

:iy Actual yields (kg/ha) 3,187.57 1,712.66 4,864.67 1,744.65 2,675.34 1,538.78 3,061.79 1,255.16 2,813.08 1,414.98 1,718.60 969.85

:eiy Expected yields (kg/ha) 2,520.76 1,164.42 3,124.86 1,314.80 2,495.60 1,048.41 2,722.69 912.37 2,065.28 919.38 1124.23 1,039.80

evy1 : Yield risk (unitless) 674.125 1,078.684 1,116.002 2,714.136 1,542.151 576.417 1,820.589 715.485 766.703 1,482.178 265.690 742.097

:iA Multiply imputed area planted of crop i

(ha)

0.136

0.469

0.189

0.719

0.178

0.673

0.102

0.701

0.138

0.566

0.111

0.365

:is Multiply imputed acreage share of crop i

(%)

0.120

0.191

0.151

0.196

0.137

0.177

0.088

0.132

0.130

0.166

0.090

0.131

:ip Market price of crop i (Ushs/kg), deflated

by UBOS’ All items consumer price index

404.937

163.655

566.410

205.772

780.087

215.044

439.861

152.87

993.879

231.798

1,258.768

344.449

:,

e

iNp Expected output price of crop i from

naive expectations model

392.320

204.261

516.690

226.659

739.508

220.706

437.842

122.563

975.849

295.929

1238.239

377.296

:,

e

iRp Expected output price of crop i, rational

expectations model (ARIMA model)

373.550

138.792

525.429

196.176

760.973

239.576

423.196

124.186

968.780

226.281

1222.099

330.374

:,

e

iAp Expected output price of crop i, adaptive

expectations model

388.770

154.727

490.462

201.653

703.204

189.053

423.870

127.223

953.207

253.796

1,186.577

347.950

:,

e

iMXp Expected output price of crop i, mixed

expectations model (with optimal )

383.659

104.889

526.517

164.223

750.834

199.748

424.179

89.293

957.878

229.497

1,220.348

303.900

:,

e

iNvp Expected price risk of crop i using

naive expectations model

187.582

131.765

137.599

92.821

174.200

85.952

112.213

82.322

144.582

79.572

244.325

185.538

:,

e

iRvp Expected price risk of crop i using

rational expectations model (ARIMA model)

119.366

94.710

110.382

77.122

159.386

81.420

90.405

71.322

126.595

70.387

196.606

169.701

:,

e

iAvp Expected price risk of crop i using

adaptive expectations model

206.288

134.715

195.269

127.616

236.437

118.922

152.973

117.996

190.274

109.491

346.534

253.844

:,

e

iMXvp Expected price risk of crop i using

mixed expectations model

164.892

104.948

145.512

88.527

205.962

92.786

122.062

89.347

154.489

72.580

302.576

214.757

Note: SD: Standard deviations

Appendices

206

Appendix C.8 Dynamic Multivariate fractional logit estimation results – Models with (I) and without (II) unobserved heterogeneity


I II I II I II I II I II I II

1,1 ts 0.313* 0.324 -0.038 -0.079 -0.078 -0.101 -0.069 -0.023 -0.184 -0.201 -0.193 -0.200

1,2 ts -0.465** -0.477** 0.412*** 0.437*** -0.007 -0.039 -0.299* -0.343** -0.298* -0.328* -0.062 -0.098

1,3 ts -0.378* -0.389* -0.510 ** -0.515** 0.424** 0.429** -0.584*** -0.589*** -0.561*** -0.579*** -0.596*** -0.616***

1,4 ts -0.151* -0.170* -0.261** -0.264* -0.412* -0.432* 0.572*** 0.591*** -0.101 -0.107 -0.099*** -0.103***

1,5 ts -0.698*** -0.725*** -0.431** -0.469** -0.489** -0.471** -0.582*** -0.638** 0.678*** 0.682*** -0.625** -0.635**

1,6 ts -0.686** -0.724** -0.226 -0.263 -0.085 -0.098 -0.422* -0.447* -0.189 -0.192 0.366* 0.364*

1,1s 2.861 *** 2.927*** 1.277*** 1.337*** 1.580*** 1.644*** 1.867*** 1.937*** 2.105*** 2.149*** 1.329*** 1.388***

1,2s 0.727*** 0.780*** 1.960*** 1.966*** 1.332*** 1.344*** 1.345*** 1.374*** 1.086*** 1.088*** 1.130*** 1.144***

1,3s 1.379*** 1.416*** 1.613*** 1.637*** 2.704*** 2.733*** 1.679*** 1.702*** 1.726*** 1.748*** 1.625*** 1.648***

1,4s 1.460*** 1.514*** 1.136*** 1.185*** 1.439*** 1.481*** 2.903*** 2.944*** 1.412*** 1.441*** 1.049*** 1.096***

1,5s 2.511*** 2.538*** 1.602*** 1.607*** 1.752*** 1.753*** 1.830*** 1.815*** 2.690*** 2.691*** 1.577*** 1.596***

1,6s 1.235*** 1.314*** 0.993*** 1.028*** 1.219*** 1.253*** 1.172*** 1.200*** 1.277*** 1.291*** 2.408*** 2.412***

ep1 0.364*** 0.365*** 0.072*** 0.072*** 0.087*** 0.087*** 0.088*** 0.089*** 0.104*** 0.105*** 0.061*** 0.061***

ep2 0.081*** 0.082*** 0.352*** 0.349*** 0.095*** 0.097*** 0.094*** 0.097*** 0.090*** 0.093*** 0.080*** 0.084***

ep3 0.051*** 0.052*** 0.069*** 0.068*** 0.397*** 0.396*** 0.069*** 0.066*** 0.064*** 0.064*** 0.054*** 0.054***

ep4 0.027*** 0.027*** 0.031*** 0.030*** 0.032*** 0.031*** 0.449*** 0.450*** 0.027*** 0.028*** 0.017*** 0.016**

ep5 0.112*** 0.114*** 0.070*** 0.071*** 0.068*** 0.069*** 0.072*** 0.073*** 0.405*** 0.404*** 0.050*** 0.051***

ep6 0.049*** 0.048*** 0.057*** 0.058*** 0.055*** 0.056 *** 0.056*** 0.056*** 0.054*** 0.054*** 0.422*** 0.421***

ey1 8.605*** 8.376*** 8.279*** 8.760*** 7.423*** 7.523*** 9.063*** 9.949*** 7.228*** 6.182*** 6.741*** 6.506***

ey2 6.502 5.042 10.189*** 10.894*** 11.680*** 11.372*** 13.052*** 13.806*** 9.175*** 9.432*** 9.142*** 9.913***

ey3 1.282 1.069 6.817*** 5.184*** 6.020*** 6.635*** 7.813*** 7.696*** 5.315*** 5.528*** 5.860*** 6.603***

ey4 5.974* 5.918* 9.833*** 9.095*** 9.368*** 9.525*** 11.572*** 11.895*** 8.762*** 8.005*** 8.069*** 7.548***

ey5 1.020** 1.522* 1.395*** 1.518*** 1.496*** 1.640*** 1.387*** 1.069*** 1.792*** 1.955*** 1.324*** 1.808***


207

Appendix C.8 (continued)


I II I II I II I II I II I II ey6 3.693* 7.643* 5.382* 5.379* 6.294** 6.326** 10.314*** 10.368*** 7.097*** 7.139*** 5.337* 5.251

evp1 -4.676*** -4.593*** -4.742*** -4.737*** -4.854*** -4.785*** -5.665*** -5.695*** -4.347*** -4.263*** -4.079*** -3.935***

evp2 -3.887*** -3.780*** -3.421*** -3.458*** -3.671*** -3.605*** -4.105*** -4.142*** -2.845*** -2.761*** -3.510*** -3.379***

evp3 -4.076*** -4.003*** -3.382*** -3.379*** -3.296*** -3.234*** -4.071*** -4.087*** -3.144*** -3.076*** -2.786*** -2.655***

evp4 -4.717*** -4.640*** -3.832*** -3.861*** -3.998*** -3.954*** -4.934*** -4.964*** -3.536*** -3.464*** -3.506*** -3.401***

evp5 -4.059** -2.002* -3.177*** -3.004*** -3.421* -3.002** -4.0195* -4.017** -3.325** -3.568* -3.251* -2.011

evp6 -2.021*** -1.056 -3.115 -3.000* -3.804*** -2.058* -4.751*** -1.348*** -3.867*** -3.195* -3.498** -2.025***

evy1 -0.142*** -0.108*** -0.114*** -0.089*** -0.089*** -0.075*** -0.091** -0.069** -0.111*** -0.079** -0.086** -0.036

evy2 -0.059*** -0.034 -0.023*** -0.006* -0.042*** -0.024 -0.069* -0.037 -0.043* -0.030 -0.077* -0.025

evy3 -0.044 -0.027 -0.051 -0.049 -0.046* -0.048* -0.036 -0.035 -0.064* -0.046 -0.098* -0.078*

evy4 -0.060* -0.021 -0.462* -0.047 -0.543 -0.042 -0.107* -0.052 -0.168* -0.035 -0.156 -0.012

evy5 -0.012* -0.044 -0.039* -0.000 -0.013 -0.069* -0.037 -0.030 -0.130*** -0.061* -0.042 -0.066*

evy6 -0.121*** -0.080*** -0.119*** -0.097*** -0.095*** -0.741** -0.144*** -0.122*** -0.107*** -0.086*** -0.140*** -0.128***

mar -0.006 -0.074 -0.035*** -0.016* 0.040*** 0.052*** 0.015*** 0.019*** 0.037*** 0.049*** -0.010 -0.030*** marcv -8.639*** -8.522*** -5.129*** -5.176*** -4.907*** -4.840*** -5.722*** -5.750*** -4.591*** -4.492*** -4.589*** -4.475***

dmt -2.947** -3.549* -4.431*** -6.185*** -4.438*** -6.528*** -5.252*** -8.002*** -4.415*** -5.880*** -2.170 -3.970***

dmtcv -3.523 -3.493 -9.317*** -9.143*** -6.658*** -6.551*** -9.971*** -10.050*** -8.559*** -8.571*** -6.642*** -6.242***

tld 0.702*** 0.688*** 0.695*** 0.682*** 0.619*** 0.614*** 0.712*** 0.701*** 0.692*** 0.690*** 0.703*** 0.706***

ldq 0.024* 0.054 0.048* 0.102** 0.077** 0.148*** 0.051* 0.145*** 0.057* 0.131*** 0.067** 0.126**

ldir 0.204 0.112 0.098 0.204* 0.099 0.040 0.144 0.049 0.157 0.124 -0.106 -0.157

ldsp 0.149 0.147* 0.014 0.044 0.017 0.047 0.103 0.149* 0.038 0.133* 0.091 0.129

educ 0.018 -0.002 0.007 -0.003 0.013 -0.011* 0.011 -0.007 0.020 -0.007 0.012 -0.022*** age -0.381* 0.145 -0.167 -0.015 -0.314 -0.040 -0.074 0.007 -0.156 0.025 0.013 0.085 sex 0.048 0.059 -0.103 0.099* -0.111 0.095* -0.193 0.102* -0.123 0.043 -0.139 0.067

0.206*** 0.230*** 0.812*** 0.839*** 0.259*** 0.320*** 0.553*** 0.625*** 0.645*** 0.698*** 0.253*** 0.385***

hsz 0.143* 0.042 0.109** 0.074 0.045* 0.005 0.058** 0.025 0.067* 0.012 0.052* 0.011

Cons 29.106 27.422 39.894*** 31.344*** 88.980*** 39.160*** 56.563*** 40.809*** 74.488*** 28.303*** 23.729*** 27.344***

Note: In models I, unobserved heterogeneity is allowed to be correlated with some variables and the Mundlak-Chamberlain approach has been applied. In models II, unobserved

heterogeneity is ignored during estimation. To preserve space, coefficient parameters of time-averaged variables have been omitted from the table but are available upon author’s request.

Results are obtained after normalization of the coefficients of “other crops” share. ***

, **

, and * denote statistical significance at 10, 5, and 1% levels, respectively.

Appendices

208

Appendix C.9 Static Multivariate fractional logit estimation results – Models with (I) and without (II) unobserved heterogeneity


I II I II I II I II I II I II ep1 0.409*** 0.416*** -0.068*** -0.064*** -0.081*** -0.078*** -0.083*** -0.081*** -0.079*** -0.076*** -0.059*** -0.056***

ep2 -0.106*** -0.117*** 0.365*** 0.359*** -0.112*** -0.123*** -0.113*** -0.127*** -0.108*** -0.121*** -0.103*** -0.122***

ep3 -0.062*** -0.064*** -0.056*** -0.054*** 0.436*** 0.440*** -0.057*** -0.056*** -0.062*** -0.063*** -0.046*** -0.045***

ep4 -0.048*** -0.053*** -0.043*** -0.048*** -0.038*** -0.042*** 0.461*** 0.463*** -0.045*** -0.049*** -0.032*** -0.037***

ep5 -0.069*** -0.069*** -0.054*** -0.056*** -0.050*** -0.051*** -0.054*** -0.055*** 0.448*** 0.453*** -0.039*** -0.043***

ep6 -0.060*** -0.058*** -0.071*** -0.072*** -0.071*** -0.070*** -0.065*** -0.062*** -0.064*** -0.061*** 0.457*** 0.469***

ey1 11.629*** 12.146*** 12.027*** 15.748*** 12.740*** 18.848*** 13.285*** 15.561*** 12.395*** 14.764*** 11.376*** 11.353***

ey2 7.168 5.276 15.723*** 17.570*** 18.653*** 18.986*** 19.723*** 14.938*** 18.058*** 12.699*** 16.794*** 17.083***

ey3 1.582 0.845 8.299*** 7.314*** 10.388*** 7.391*** 11.122*** 9.227*** 10.097*** 7.942*** 9.362*** 6.149***

ey4 9.808*** 6.203* 14.124*** 8.165*** 15.961*** 16.095*** 16.786*** 11.582*** 15.493*** 17.910*** 14.293*** 8.831***

ey5 1.930*** 1.661* 2.493*** 6.912*** 2.764*** 5.303*** 2.849*** 6.507*** 2.639*** 6.344*** 2.503*** 3.358***

ey6 4.878 3.760 5.572** 6.250** 9.068*** 9.785*** 12.014*** 12.714*** 10.863*** 11.398*** 7.023** 7.428**

evp1 -6.400*** -3.797*** -7.021*** -4.364*** -7.760*** -4.875*** -8.120*** -5.309*** -7.557*** -4.638*** -6.864*** -3.753***

evp2 -5.829*** -2.965** -6.241*** -3.356*** -6.940*** -3.783*** -6.880*** -3.795*** -6.259*** -3.097*** -6.568*** -3.197***

evp3 -5.504*** -3.195*** -5.356*** -3.025*** -5.712*** -3.201*** -6.055*** -3.606*** -5.725*** -3.164*** -5.058*** -2.398***

evp4 -6.854*** -3.993*** -6.594*** -3.736*** -7.286*** -4.190*** -7.692*** -4.642*** -7.077*** -3.913*** -6.562*** -3.278***

evp5 -5.049** -3.020* -4.107*** -3.054*** -5.035* -4.032** 6.003 2.003 -5.043** -4.002 -5.051* -3.001

evp6 5.011*** 3.023 4.015 -3.014 -5.084*** -4.018 -6.079*** -2.005*** -5.123*** 4.001 -5.098** -4.005***

evy1 -0.277*** -0.113*** -2.570*** -0.103*** -0.256*** -0.090*** -0.249*** -0.081*** -0.266*** -0.093*** -0.265*** -0.057***

evy2 -0.463*** -0.388*** -0.403*** -0.430*** -0.447*** -0.348*** -0.498*** -0.463*** -0.476*** -0.288*** -0.517*** -0.058***

evy3 -0.205*** -0.173* -0.178*** -0.028* -0.167*** -0.173*** -0.204*** -0.251*** -0.203*** -0.032* -0.245*** -0.067*

evy4 -0.598*** -0.124* -0.654*** -0.829** -0.666*** -0.727* -0.607*** -0.418** -0.683*** -0.628* -0.633*** -0.408*

evy5 -0.097** -0.059* -0.092* -0.023* -0.147*** -0.084** -0.099** -0.049* -0.142*** -0.085** -0.220*** -0.071*

evy6 -0.416*** -0.087** -0.401*** -0.469*** -0.372*** -0.256* -0.445*** -0.112*** -0.409*** -0.417** -0.416 -0.100***

mar -0.026 -0.080 -0.049*** -0.020* 0.043*** 0.059*** 0.035*** 0.029*** 0.040*** 0.056*** -0.019 -0.031***


209

Appendix C.9 (continued)


I II I II I II I II I II I II

marcv -10.544*** -6.866*** -8.375*** -4.753*** -8.447*** -4.513*** -8.569*** -4.771*** -8.221*** -4.290*** -7.731*** -3.729***

dmt 0.3037 -0.103 -0.647*** -0.253* -0.498*** 0.756*** -0.704*** 0.368*** -0.717*** 0.712*** -0.285 -0.392***

dmtcv -5.189** -3.759* -10.504*** -8.251*** -9.554*** -7.528*** -12.522*** -10.702*** -12.034*** -9.848*** -9.570 -6.900***

tld 0.384*** 0.848*** 0.365*** 0.812*** 0.255*** 0.725*** 0.377*** 0.879*** 0.324*** 0.832*** 0.299*** 0.815***

ldq 0.132** 0.081* 0.156*** 0.138*** 0.194*** 0.179*** 0.166*** 0.203*** 0.170*** 0.181*** 0.190*** 0.139***

ldir 0.134 0.168 0.092 0.284** 0.086 0.121 0.112 0.072 0.117 0.153 -0.070 -0.082

ldsp 0.061 0.181* 0.126 0.131 0.142 0.055 0.076 0.202** 0.150 0.192** 0.081 0.211**

educ 0.008 0.003 0.011 0.003 0.014 -0.006 0.001 -0.006 0.011 -0.003 0.009 -0.038*** age 0.043 -0.041 0.291 -0.205** 0.143 -0.342*** 0.374 -0.210** 0.312 -0.220** 0.471 -0.186* sex 0.225 0.053 0.097 0.134** 0.069 0.096 0.042 0.029 0.091 0.029 0.117 0.095

0.951*** 0.845*** 0.766*** 0.739*** 0.148*** 0.951*** 0.455*** 0.421*** 0.457*** 0.429*** 0.419*** 0.522****

hsz 0.462*** 0.119* 0.426*** 0.160*** 0.324*** 0.126** 0.400*** 0.173*** 0.404*** 0.094* 0.436*** 0.152***

Cons 18.451 43.421 44.108*** 45.249*** 53.119*** 20.801*** 57.605*** 94.041*** 52.647*** 21.793*** 47.028*** 31.802***

Note: In models I, unobserved heterogeneity is allowed to be correlated with some variables and the Mundlak-Chamberlain approach has been applied. In models II, unobserved

heterogeneity is ignored during estimation. To preserve space, coefficient parameters of time-averaged variables have been omitted from the table but are available upon author’s request.

Results are obtained after normalization of the coefficients of “other crops” share. . ***

, **

, and * denote statistical significance at 10, 5, and 1% levels, respectively.

Appendices

210

Appendix D

Additional data and estimation results for Essay IV


211

Appendix D.1 Cumulative distributions and growth rates of households’ welfare

Appendices

212

Appendix D.2 Test of equality between households above and below the vulnerability index hvul

jax j

bx

jx jb

j xx / Equality test

1j 0.783

(0.139)

0.544

(0.221)

0.240 0.441 77.069

[0.000]***

2j 0.585

(0.312)

0.398

(0.281)

0.188 0.471 40.387

[0.000]***

3j 23,501

(19,311)

87,197

(161,592)

-94,379 -0.801 -220

[0.000]***

4j 3.435

(3.217)

6.038

(4.229)

-2.603 -0.431 -36.247

[0.000]***

5j 7.285

(3.470

7.298

(3.676)

-0.013 -0.002 -0.172

[0.864]

Note: j

ax and j

bx denote the reported values of the characteristic j for households above and below the vulnerability

threshold, respectively. j

bj

aj xxx . The equality test is a t-test with unequal variances checking whether the mean

values of the characteristic j are significantly different between households above and below the threshold hvul .

Standard deviations and standard errors are reported into parentheses and into brackets, respectively. ***

indicates

coefficients statistically significant at 1% level. The characteristics under investigation include: 1j : Food dependency,

measured by the ratio of food consumption to total household expenditures; 2j : Market participation, approximated by

the share of food purchased into total value of food consumption; 3j : monthly real income per adult equivalent; 4j :

Years of education of the head; 5j : Household size.